Is $f (x) = (x + 3) (x - 2) (x + 4)$ $f(x)=(x+3)(x-2)(x+4)$ increasing or decreasing at $x = - 1$ $x=-1$ ?

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Answer 1 · 2018-07-17T09:13:22

$f'(-1)=-9<0$ so the function is decreasing at $x=-1$

Given $f(x)=(x+3)(x-2)(x+4)$
expanding the Right-Hand side:

$(x+3)(x-2)(x+4)=(x^2+3x-2x-6)(x+4)=(x^2+x-6)(x+4)=x^3+x^2-6x+4x^2+4x-24$

$f'(x)=x^3+5x^2-2x-24$

$f'(x)=3x^2+10x-2$
and

$f'(-1)=3-10-2=-9<0$

Is f(x)=(x+3)(x-2)(x+4)f(x)=(x+3)(x−2)(x+4)f(x)=(x+3)(x-2)(x+4) increasing or decreasing at x=-1x=−1x=-1?