Calculus

Problem 1. (1 point) Consider the function f(x) = 213 + 4x2 - x - 3 Find the average rate of change of this function on the interval (4, 10). By the Mean Value Theorem, we know there exists a c in the open interval (4, 10) such that f'(c) is equal to this average rate of change. Find the value of c in the interval which works Note: You can earn partial credit on this problem. preview answersProblem 2. (1 point) Consider the function f(x) = - 3+ er (A) Find the first derivative of f. f'(x) = (B) Use interval notation to indicate where f() is increasing. NOTE: Use 'Inf for oo, '-Inf for -oo, and use "U' for the union symbol. Increasing: (C) List the x coordinates of all local minima of f. If there are no local maxima, enter "NONE. I values of local minima: (D) List the a coordinates of all local maxima of f. If there are no local maxima, enter 'NONE". T values of local maxima: (E) Find the second derivative of f: f" (I) = (F) Use interval notation to indicate the interval(s) of upward concavity of f(I). Concave up: (F) Use interval notation to indicate the interval(s) of downward concavity for f(I) Concave down: (G) List the c values of the inflection points of f. If there are no inflection points, enter "NONE'. I values of inflection points: Note: You can earn partial credit on this