Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x) = x^3 + 6x^2 − 15x

Question

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x) = x^3 + 6x^2 − 15x

tkhunny · Answer

Have you considered 1st and 2nd derivatives?

anonymous · Answer

Yes, I know how to get the first and second derivatives, but I'm unsure if I need to make f(x) 0 or just plug in 0 for x for the the derivatives.

anonymous · Answer

@tkhunny

tkhunny · Answer

There is no such thing as "plug in".

Find where the two derivatives are zero and make the determination.  How have you defined "critical number"?  Is it just "x = something" or is it "(x,f(x))"?

anonymous · Answer

take the derivative
set it equal to zero and solve for $x$

anonymous · Answer

you will get a quadratic equation and so it will probably have two zeros