Question

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

Answer 1

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`