Question

Is `f(x)=(x+2)(2x-3)(x-2)` increasing or decreasing at `x=0`?

Answer 1

`f darr` at `x=0`.

Explanation:

`f(x)=(x+2)(2x+3)(x-2)=(2x+3)(x^2-4)=2x^3+3x^2-8x-12`

Now, we know that, `f'(a)>0 rArr f uarr` at `x=a`, and,

`f'(a)<0rArr f darr` at `x=a`.

So, let us check `f'(0)`

`f'(x)=6x^2+6x-8 rArr f'(0)=-8<0`

Hence, `f darr` at `x=0`.