Is f(x)=(x-16)(x-12)(x/4+3) increasing or decreasing at x=1?

1 Answer
Jan 8, 2016

The gradient is negative so the function is decreasing

Explanation:

First expand the expression to simplify it, then differentiate to find the gradient. The gradient is negative if the function is decreasing and positive if it is increasing.
f(x) = (x-16)(x^2/4 -36) = (x^3/4 -4x^2 - 36x + 576)
f'(x) = (3x^2)/4 -8x -36
f'(1) = 3/4 - 8 -36 = -43*1/4