Is #f(x)=(x-3)(x+5)(x+2)# increasing or decreasing at #x=-3#?

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Answer 1 · 2015-12-06T23:22:22

The function is decreasing.

The answer lies if the first derivative. If it is positive at #x=-3#, the function is increasing, if it is negative, it's decreasing.

It's easier to compute the derivative of the expanded form, and we have that #(x-3)(x+5)(x+2)=x^3+4 x^2-11 x-30#

So, the first derivative is

#f'(x)=3x^2+8x-11#

Evaluating #f'(-3)#, we have

#3(-3)^2 +8(-3)-11 = 3*9 -24-11 = 27-24-11=-8#

So, the function is decreasing.