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- Let h be the function h(x) = 2x2. The value of x decreases as x changes from −2 to −1. TRUE OR FALSE As x changes from −2 to −1, h(x) changes from .... to .... As x changes from −1 to 1, h(x) changes from .... to .... 4. The average rate of change of h on the interval from −1 to 1 is greater than the average rate of change of h on the interval from −2 to −1. TRUE OR FALSE? Justify by calculating both average rates of change. Show all work. 5. Mark the correct answer. h(x) is concave up. concave down. neither. both PLEASE HELP ME WITH THEM ALL. THANK YOUUShow that a constant function f1x2 = b has an averagerate of change of 0. Compute the average rate of changeof y = 24 - x2 on the interval 3 - 2, 24. Explain how this can happen.Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate of change of y = √(4 - x2) on the interval [ - 2, 2]. Explain how this can happen.
- What is the average rate of change of the function f ( x ) = 3 x over the interval [ 2 , 5 ]Find the average rate of change of the function f ( x ) = 1 x2 − 4 x + 4 , on the interval x ∈ [2,4].The derivative of ƒ(x) = x2 is zero at x = 0, but ƒ is not a con-stant function. Doesn’t this contradict the corollary of the Mean Value Theorem that says that functions with zero derivatives are constant? Give reasons for your answer.
- Find the average rate of change of the function from x1 to x2. function x-value f(x) = x2 − 2x + 7 x1 = 1, x2 = 5Make a table of values for the function F(x) = (x + 2)/(x - 2)at the points x = 1.2, x = 11/10, x = 101/100, x = 1001/1000,x = 10001/10000, and x = 1. Find the average rate of change of F(x) over the intervals [1, x] for each x ≠ 1 in your table.Find the exact location of all the relative and absolute extrema of the given function. f(x) = x − ln(x) with domain (0, +∞) The variable f has ---Select--- at (x, y) =
- Find the critical points of the function. Then use the Second Derivative Test to determine whether they are local minima, local maxima, or saddle points (or state that the test fails). f (x, y) = x ln(x + y)Compute the relative rate of change for a power function, that is, a function of the form f(x) =Ax^n for positive constants A and n. Analyze the relative rate of change as x →∞, and interpretthe resultFind all the critical points of function below and use second derivative test to label them f(x,y) = xln(x^2+y^2) Show all work by hand (or typed) and explain every step.