Consider the equation below. f(x) = 2x3 + 3x2 - 72x Find the interval on which f

Question

Consider the equation below. f(x) = 2x3 + 3x2 - 72x Find the interval on which f is increasing. (Enter your answer in interval notation.) Find the interval on which f is decreasing. (Enter your answer in interval notation.) Find the local minimum and maximum values of f. local minimum local maximum Find the inflection point. (x, y) = ( ) Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down. (Enter your answer in interval notation.)

Explanation / Answer

a)f(x)=2x^3+3x^2-72x =>f' = 6x^2+6x-72 = 6(x^2+x-12) = 6(x+4)(x-3) = 0 =>x = -4,3 f is increasing in (-infinity,-4) U (3,infinity) b)f'' = 12x+6 f''(-4) < 0........local maximum = 208 f''(3) > 0 .......local minimum = -135 c)Point 0f inflection: x = -6/12 = -0.5 concave up: (-0.5, infinity) concave down: (-infinity, -0.5)

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