# Is f(x)=(x+1)(x-4)(x-2) increasing or decreasing at x=1?

Dec 14, 2015

Decreasing

#### Explanation:

Original equation :
$f \left(x\right) = \left(x + 1\right) \left(x - 4\right) \left(x - 2\right)$

foil:
$f \left(x\right) = \left({x}^{2} - 3 x - 4\right) \left(x - 2\right)$
$f \left(x\right) = \left({x}^{3} - 5 {x}^{2} + 2 x + 8\right)$

Derive:
${f}^{'} \left(x\right) = \left(3 {x}^{2} - 10 x + 2\right)$

Plug in x:
${f}^{'} \left(1\right) = \left(3 {\left(1\right)}^{2} - 10 \left(1\right) + 2\right)$
${f}^{'} \left(1\right) = \left(3 - 10 + 2\right)$
${f}^{'} \left(1\right) = \left(- 5\right)$

${f}^{'} \left(1\right)$ is negative, so $f \left(x\right)$ is decreasing at $x = 1$