Determine the critical numbers of the given function

[Fender]

and classify each critical point as a relative maximum, a relative minimum or neither.

f(t)= 2t^3 + 6t^2 + 6t + 5

Can someone answer this and explain it to me step by step? I'm having a hard time understanding it..... I'm taking a calculus class this summer and I'm finding it difficult.

 

[daon]

Do you know what a critical number is or the gist of how to find them? Have you tried to do this problem? Give us something to work with...

 

[stapel]

Can someone answer this and explain it to me step by step?

Follow the steps they gave you in your book and in your class.

i) Take the derivative. Set it equal to zero; solve for the critical points.

ii) Take the second derivative. Set it equal to zero; solve for possible inflection points.

iii) Apply the First and Second Derivative tests.

Please reply showing how far you have gotten in the steps. Thank you!

 

[BigGlenntheHeavy]

If f is defined at c, then c is called a critical number of f if f ' (c)=0 or if f ' is undefined at c.

Hence f(t) = 2t^3+6t^2+6t+5, f ' (t) = 6(t+1)^2, f ' (-1) = 0

Now -1 is a critical number and f(-1) = 3.

I'll leave it up to you to decide if -1 yields a rel. max., a rel min, or neither.

Hint: One way, look at the graph of f(t).