Question
Consider the function f(x) = -2 x^3 + 42 x^2 - 240 x + 11. For this function there are three important intervals: (-inf, A), (A,B), and (B,inf) where A and B are the critical values. Find A=? and B=? For each of the following intervals, tell whether f(x) is increasing (type in INC) or decreasing (type in DEC). (-inf, A): ? (A,B): ? (B,inf) ? f(x) has an inflection point at x =C where C is Finally for each of the following intervals, tell whether f(x) is concave up (type in CU) or concave down (type in CD). (-inf, C): ? (C,inf) ?
Explanation / Answer
Decreasing on 4) since f'(x) < 0 Increasing on (4, 10) since f'(x) > 0 Decreasing on (10, since f'(x) < 0