Is f(x)=(x-3)(x+15)(x+2)f(x)=(x3)(x+15)(x+2) increasing or decreasing at x=-1x=1?

1 Answer
Jun 23, 2016

ff is decreasing at x=-1.x=1.

Explanation:

For a fun. f, f'(a)>0 rArr f is incrs. at a.

For a fun. f, f'(a)<0 rArr f is dcrs. at a.

f(x)=(x-3)(x+15)(x+2) =x^3+(-3+15+2)x^2+{-3*15+15*2+(-3)*2}x+(-3)*15*2
=x^3+14x^2-21x-90.

Hence, f'(x)=3x^2+28x-21 rArr f'(-1)=3-28-21=-46<0.

So, f is decreasing at x=-1.

An easy way to find f'(x) is to use the Rule : (uvw)'=u'vw+uv'w+uvw'.

By this Rule, f'(x)=(x+15)(x+2)+(x-3)(x+2)+(x-3)(x+15) giving,
f'(-1)=14*1+(-4)*1+(-4)14=14-4-56=-46, as before!