5. Find all stationary points of the following function. For each stationary point, determine if it is a local maxima, a local minima, or neither. y = (x + 1)6 + (x + 1)7.
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- The line in the graph shows a relationship between two variables, x and y. What is the slope of the curve? ... The slope of the curve is >>> If the slope is negative, use a minus sign. If the slope is positive, do not use a plus sign. 8 7 5- 4- 3- 2- 1- 0- y 0 1 2 3 4) Find and classify the stationary points of the following function: f (x) = 1. [Specify the 1st and 2nd order conditions.] 1. T-16). Compute the directional derivative of function f(x,y) = xy³ + 2.x²y at the point (2, 1) in the direction (,, ).
- Consider the function Y = *square root*pXZ where X > 0 and Z > 0. Draw the contour lines (in the positive quadrant) for this function for Y = 4, Y = 5, and Y = 10. What do we call the shape of these contour lines? Where does the line 20X + 10Z = 200 intersect with the contour lineY = 50?Compute the first and second derivatives of the following functions of x. In each case, determine whether the function has any local extremes (maxima or minima) on the domain of nonnegative real numbers – i.e. for x E [0, 0). a. f(x) = 4 + 3x? b. f(x) = x (4x – 3) (9 - 5x) с. f(x) — x2 d. f(x) = In(x) -Colton is trying to figure out when two buses traveling at different speeds will pass one another. The buses are traveling in the same direction and begin 3 miles apart. He has defined variable tt as follows: Let tt represent the time in hours. Is this a good variable definition? YES OR NO ? IF NO than explain why?
- If A is the dependent variable and B is the independent variable, then a change in A results in a change in B. 1) True 2) FalseConstruct a table from the data shown on the graph below. Which is the dependent variable and which the independent variable? Summarize the data in equation form.Draw a graph of a relationship that has a minimum y- value of 1 when the X-value is 5. y 9- Use the point tool to plot the minimum point of the relationship. Now use the 3-point curve tool to draw a curve that shows a minimum value at this point. 5- 4- 3- 10 11 12 (1,0) >>> Draw only the objects specified in the question.