(b) Find the linearization of function S(x) = Vx V220 at a=216 and use approximate number (c)Find the absolute maximum and minimum values of function f(x)= 4x* - 2.x² +3 -2

Q: 2/3 Q31 3x-2x, [-1,1] =3(x)-2 2- -1/3 -1/3 2x 2(x"?-1)=0 -1/3

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Q: In the function:  f(x)=(12−3x)e^x  What are the critical numbers of the function?  When is the…

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Q: f(x) = sin 2x,x e [0,2n]

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Q: FIND THE MINIMUM AND MAXIMUM VALUE F (X) = X/(1-X) X e(0,1)

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Q: Let f(x) = 2(x − 1)^2 (2x + 1) be a function. Find all critical numbers of the function and…

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Q: 3:- Find the maximum value of the function f(x, y) = x²y on the line x + y = 3.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The function f(x, y) = 2x² + y² – 3xy – 2x + y – 2 has one critical point. Find it, and determine if…

A: take the partial derivative with respect to x

Q: Find all the critical points of the function f(x;y)=.x3+y3-3xyDetermine if they are local…

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Q: Find the critical numbers of the function. y- 2 g(y) = %3D y2 - 2y + 4

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Q: 1. Find and classify all critical points of the function f(x, y) = x² + y²-3x - 4y.

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Q: Consider the function f(x) = 648x¬² + x³. Taking the initial point as x = 6 and increment value as…

A: Here, fx=648x2+x3 Take x0=6 and △=1 Iteration 1) k=0 of xk Now, xk+1=xk+2k△ Here, x0=6…

Q: Show that the function f(x) = e1/2)[(x-µ)/a}° has a relative maximum at x = µ.

A: fx=e-12x-μσ2 Differentiating with respect to x, we get…

Q: Find the critical point of the following function y= -x2 + 2x - 2

A: Given: The function y=-x2+2x-2, To find: The critical point of the given function.

Q: 2. Given f(x, y) = 12x2x³ + 3y² + 6xy. (i) Find critical points of f. (ii) Use the second derivative…

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Q: 9. Find the local minimum and local maximum values using both the First and Second Derivative…

A: To find the local minimum and local maximum values.

Q: (b) Let f(x) = 12x35+ 15x* – 40x³ + 17. Find the critical numbers, and show what the Second…

A: f(x) = (12x 5+15x4 -40x3 +17.   critical points   f'(x) = 0   60 x4 + 60x³-120x²  = 0.   x² ( 60…

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

A: f(x) = ax3 + bx2 + cx + d f(x) = 3ax2 + 2bx + c Now, f(x) = 0  at x = -2, 1 Hence , roots of above…

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

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Q: Determine the values of constants a, b, c, and d so that ƒ(x) = ax3 + bx2 + cx + d has a local…

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Q: Given the function f(x)=x4-6x2-60x2+134x+30 The value x=1 satisfies the equation f'(x)=0 (that is,…

A: The function f(x) is maximum when f''(x)<0 at x=a The function f(x) is minimum when f''(x)>0…

Q: Find values of a and b so that the function f(x) = x + ax +b has a local minimum at the point (7, -…

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Q: Find the second iteration value of an extremum (maximum/minimum value) of f(x) = 5sin2x - bx2 - cx…

A: Given the function fx=5sin2x-2x2-4x. The initial guesses are x1=0, x2=1, x3=1.5. The Quadratic…

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x-2x²

A: We can use application of derivative order to solve the given problem.

Q: b. Find the orthogonal trajectories for the family of curves x² + y² =C².

A: we have to find the orthogonal trajectory of the given family of curve

Q: Find the relative maximum or minimum value (if any) of f(x, y) = (x2 + y)ey/2

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Q: 1. Find the critical points of the function f(x, y) = x² + 4xy. 2. Find the local maximum and…

A: f(x,y)=x2+4xy we have to find the critical points.

Q: . Determine the values of constants a and b so that f(x) = ax² + bx has an absolute maximum at the…

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Q: 3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a)  Find f"(x).   (b) Then use…

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Q: 5 Find the point X to minimize the function f(x1, x2) =1+¤1 +2x2+ from the strating point X, = using…

A: We are given the following optimization problem : f(x1 , x2) = 1 + x1 + 2x2 + 5/x1 + 10/x2 And we…

Q: Q2: Find all critical numbers of the function f(x) = (x- 2)2/3 +1 and classify each critical point…

A: Here we will find out the required value.

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x²

A: Points of local extremum can be calculated by using the first derivative. These are points which…

Q: Find the absolute maximum and minimum values of the function y = 10x(2 – In x) on t interval (0,…

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Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

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Q: Find the maximum of U.  Find the optimum using the the Lagrangian method: U=(x+3)(y+5) subject to…

A: Given, Ux,y=x+3y+5 with the constraint Vx,y=3x+2y-30.Using Lagrange mulitplier'sUx=λVxy+5=λ3y=3λ-5…

Q: for the funciton f(x) = x^3 - 75x Its local maximum  is____, which occurs at _____> Its local…

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Q: 3. Find the Absolute Minimum and Absolute Maximum of f(x,y)=xy subject to 2x² +8y² =144 Fully…

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Q: Find a cubic function f(x) = ax + bx2 + cx + d that has a local maximum value of 4 at x = -3 and a…

A: Here we have to find the cubic function that has a local maximum value of 4 at x= -3 and a local…

Q: Find the values of constants a, b, and c so that the graph of y = ax + bax2 + cx has a local maximum…

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Q: Find the critical points of y= 2x^3 +3x^2–12x and apply the Second Derivative Test to find the…

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Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

Q: ve maximum or

A: Maxima and minima: Let f(x)=e3x2+4 For maxima or minima we need to find those values where f'(x)=0.…

Q: Calculate the difference d between the global maximum and global minimum values of f(x)=x2−4x+6 in…

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Q: 3. Find a linear approximation to the function at the point x = 3. y = f(x) = x²e + 8x

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Q: 3. Find the critical points of the function f(x,y)=xln(x+y) Use the Second Derivative Test to…

A: The given problem is to find the critical points of the given function and use second derivative…

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local maximum at x = -1 and a local minimum…

A: Given: fx=x3+ax2+bx To find a, b such that function has local maxima at x = -1 and local minima x =…

Q: The function h(x) = x³ + 28x4 – 1311x³ has a critical point at x = 19. Use the second derivative…

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Q: Find all critical points for the function f(x) = (z² – 4) . %3D

A: To find the critical points of f(x), find the derivative of f(x) and equate it to zero.

Q: Find constants a and b in the function f(x) = axb such that f(-) = 1 and the function has a In(x)…

A: Given that the function is  f(x) = abx/ln(x) such that f(1/2) = 1 and the function has a local…

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A: Find the maxima and  minima using second derivative test

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.