Find all points where the function f(x) = |x|p with p > 0 is differentiable. How does your answer depend on p?

Q: Find the value of k that makes the function continuous. Justify your answer. 2x – 1, x 2

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Q: Consider the functions :  f(x)=√x and g(x)=x-1 Solve for- (f°g) (x)

A: Given:

Q: Find f′(x) and find the equation of the line tangent to the graph of f at x=3.   f(x)=7x/2x

A: Given query is to find the equation of tangent line to f(x) ate x=3.

Q: b) Find the absolute maximum and minimum values of function f(x) = (x– 2)5 over the interval [-3, 4]

A: Absolute extrema can occur either at the points of local extrema or the boundaries of the interval.…

Q: f(x) = 4x^3-(x+9)^1/2 What is the interval or intervals on which the function is differentiable on…

A: Refer  to the question the provided function is f(x) = 4x^3-(x+9)^1/2.

Q: (a) Find the critical numbers of the function f(x) = x6(x – 4)2. (b) What does the Second Derivative…

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Q: The graph of f(x) passes through the point (-1,4), The slope of the line tangent to the graph at the…

A: The slope of the tangent of the function at a point is given by the derivative of the function at…

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: f(x)=ln 5x2+4x2+1

Q: (B) Use the second derivative test to find the maxima and minima for f(2) = 22 - 15x + 1. 3 %3D

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Q: The function f is defined by f(x) = \25 – x² for -5 sx 5. (a) Find f'(x). (b) Write an equation for…

A: Given: fx=25-x2; x∈-5,5 we know that for finding derivative of given function, we differentiate…

Q: For the function f(x) = |x2 − 4|, find the critical points, test them to find extreme values. Which…

A: According to the given information, it is required to determine the extreme values of the function.

Q: 4. Find the absolute extrema for the function f(x)= on the interval -5 ≤x≤0.

A: To find the absolute extrema of the given function in the interval [-5,0].

Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: Determine the concavity and the x values where the points of inflection occur for :  y = x + 1/x -…

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Q: Determine the absolute extrema of the function f(x) = (x-3)e* on the interval -2 ≤x≤1.

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Q: What is the minimum value of F(x) = -4 sin

A: Answer and explanation is given below...

Q: At which r-values is the following function g differentiable? Explain and compute, where necessary.…

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Q: (7) For the function f (x) = 0.25x - 2r3 Find intervals of concavity and inflection points

A: From  first derivative and second derivative of the given function we can answer to this question.

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: The critical points of the function are the points where the function is defined but its first…

Q: Determine the absolute extrema of the function f(x) (x- 4)e on the interval-1 <x<4. SHOW YOUR WORK!

A: We have given f(x) = (x – 4)ex on the interval -1 ≤ x ≤ 4.

Q: On the graph of f(x) = cos x and the interval [-2n, 0), for what value of x does f(x) achieve a…

A:

Q: Given f(x) = - x² – 3x + 2, a) Use the second derivative test to classify the local extrema of f(x).…

A: We use second derivative test in part a to find local maximum and minimum  for absolute maximum and…

Q: For the function f(x), defined graphically, state the value(s) of x where the function is not…

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Q: Find k such that the line is tangent to the graph of the function  Function: f(x)=k square root x…

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Q: (A) Find the absolute maxima and minima for ,3 Y = x + 5 over [-V2, v2). (B) Use the second…

A: y = x33-x+5y' = 3x23-1y' = x2 -1x2-1 = 0x2 = 1x = ±1

Q: Find the absolute maximum of the function f(x) = x-x-x On the interval - 10 sxS2 (a) 14 (b) 13 (e)…

A: To find absolute maximum and minimu , first, we need to find critical points. These are the points…

Q: On the graph of f(x)=secx and the interval [−2π,0), for what value of x does f(x)=1? Choose all…

A: Given  Graph of f(x)=secx and the interval [−2π,0) To do Find the value of x at which f(x)=1. Choose…

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: Critical points are points where the function is defined and its derivative is zero or…

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: Solution:Given        f(x)=xe-3xTo find:(a)Critical Point(b)the open interval where the function is…

Q: f (x) = x² – 3x/3 [0,2]

A:

Q: 17 The function f is defined by f(x) = 5x - c, where c is a constant. In the xy-plane, the graph of…

A: Solve both the problem in the following way:- (i) given point will satisfy the function. (ii)…

Q: 1 For what value of x does the function g(x) =x³ – 2x² concave downward? %3D

A: Consider the function  gx=13x3−2x2

Q: On the graph of f (x) = sec x and the interval [-2x, 0), for what value of x does f(x) = 1? Choose…

A: We need find value of x for which secx=1 in the interval -2π≤x&lt;0

Q: (A) Find the absolute maxima and minima for x3 y = - x + 5 over 3 [-V2, v2]. (B) Use the second…

A: When on critical point f''&lt;0 then that critical point give local maximum value of f(x)  When on…

Q: Does knowing that a function ƒ(x) is differentiable at x = x0 tell you anything about the…

A: Does knowing that a function ƒ(x) is differentiable at x = x0 tell you anything about the…

Q: Find the critical point of the function f(x, y) = - 5 – x + 4x? + y + 3y? This critical point is a:…

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Q: the local maximum and local minimum values of f using both the First and Second Derivative Tests.…

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Q: Find the absolute extreme values of the function on the interval. 14) f(x) = ex - x, -1 sxs 2 %3D

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Q: The elevation of a path is given by f(x) = x^3 - 5x^2 + 30, measured in feet, where x measures…

A: The elevation as a function of path is given below.

Q: Need to find local and absolute maxima and minima for the equation: f(x)=(x-2)/(x^2-1) on the…

A: Local maxima is a point f(a) on function f, a with in the domian of f, such that f(a) ≥ f(x) for all…

Q: For what value of x does the function f(x) 4x attain the absolute minimum in the interval [-3,5]? А.…

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Q: Find the absolute extrema for the function f(x)=x+ on the interval 0≤x≤ 6.

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Q: For the function, find all critical numbers and then use the second-derivative test to determine…

A: Solve by derivative

Q: On the graph of f ( x ) = sec ( x ) and the interval ( -2π, 0 ], for what value(s) of x does f ( x )…

A: f(x) = 1 on, (-2π, 0] Implies, sec(x) = 1 on (-2π, 0] i.e. x = 0 on (-2π, 0] So, x = 0  The graph of…

Q: Find the average rate of change of the function f(x) - 3x – 2x – 2, on the interval 2 < x < 4.…

A: NOTE: Refresh your page if you can't see any equations. . take x=2

Q: 1. f(x) = x2 + x – 1 for all values of x %3D

A: A detailed solution is given below

Q: 6. What is a point of inflexion ? Does f(x) = x' have a point of inflexion at x = 0?

A: Given that,

Q: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of g at x=3 is…

A: Given that: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: