find the critical number for the function f(x)= x^3+3x^2-24x

Question

APPLICATION OF DERIVATIVES

FINDING CRITICAL NUMBER

Answer 1

If f'(c)=0, or is not differentiable at c, then c is a critical number. Therefore, we must set the first derivative of our function, f(x), equal to 0 and solve for x:

f(x)=x³+3x²-24x

f'(x)=3x²+6x-24

0=3(x²+2x-8)

0=(x+4)(x-2)

x=-4, x=2

Therefore, our critical numbers are x=-4 and x=2.