The graph of the function y=x^3 + 6x^2 + 7x - 2cosx changes concavity at x=....?

We're supposed to use a calculator and the answer is -1.89 but how do you find that?

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- Jan 7th 2007, 04:22 PMabcocoaconcavity
The graph of the function y=x^3 + 6x^2 + 7x - 2cosx changes concavity at x=....?

We're supposed to use a calculator and the answer is -1.89 but how do you find that? - Jan 7th 2007, 04:33 PMgalactus
Find the 2nd derivative, set to 0 and solve for x.

Solve for x. - Jan 7th 2007, 04:36 PMThePerfectHacker
- Jan 7th 2007, 04:49 PMabcocoabut....
the answer is -1.89 not -1.39...

Also my problem is solving 6x+12+2cosx=0. How do i solve this? - Jan 7th 2007, 04:57 PMThePerfectHacker
- Jan 7th 2007, 05:08 PMgalactus
PH, I think you have a small typo in your derivative. Should be

. You have

The solution is, indeed, -1.89. I ran it through the ol' TI-92 to make doubly sure.

You may use the Intermediate Value Theorem. You can try x=-1.88 and get**0.055699**

x=-1.9 and get**-0.0232895**.

Note the sign change. Therefore, you know it's between -1.88 and -1.9. Whittle away.