Homework Soursea Find the intervals on which f is increasing or decreasing
(a) Find the intervals on which f is increasing or decreasing. (b) find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflection points.
f(x)=4x^3+3x^2-6x+1
f(x)=4x^3+3x^2-6x+1
Solution
f(x) = 4x^3 + 3x^2 - 6x + 1 (a) f\'(x) = 12x^2 + 6x - 6 = 0 2x^2 + x - 1 = 0 (2x - 1)(x + 1) = 0 x = 1/2 or x = -1 f is increasing on (-8, -1), decreasing on (-1, 1/2), and increasing on (1/2, 8). (b) local maximum value of 6 at x = -2 local minimum value of -3/4 at x = 1/2 (c) f\"(x) = 24x + 6 = 0 24x = -6 x = -1/4 concave down on (-8, -1/4) and concave up on (-1/4, 8). inflection point (-1/4, 21/8)
