# Concavity, and inflection points! Help!

• Apr 7th 2008, 02:51 AM
Hibijibi
Concavity, and inflection points! Help!
Let f(x) = x^3 + ax^2 + bx + c where a, b, and c are constants with a>0 (or a=0) and b > 0.

a) Over what intervals is f concave up? Concave down?

b) Show that f must have exactly one inflection point.

c) Given that (0, -2) is the inflection point of f, compute a and c, and then show that f has no critical point.

Really lost. All help is greatly appreciated.
• Apr 7th 2008, 04:35 AM
colby2152
Quote:

Originally Posted by Hibijibi
Let f(x) = x^3 + ax^2 + bx + c where a, b, and c are constants with a>0 (or a=0) and b > 0.

a) Over what intervals is f concave up? Concave down?

Take the second derivative of the function and set it equal to zero. Solve for x. Test values between solutions of x. When \$\displaystyle f''(x) > 0\$, function is concave up. Likewise, when \$\displaystyle f''(x) < 0\$, function is concave down.

Quote:

Originally Posted by Hibijibi
b) Show that f must have exactly one inflection point.

Once again, solve for \$\displaystyle f''(x)=0\$

Quote:

Originally Posted by Hibijibi
c) Given that (0, -2) is the inflection point of f, compute a and c, and then show that f has no critical point.

Really lost. All help is greatly appreciated.

Plug and chug my friend. How are you at finding derivatives?
• Apr 7th 2008, 04:37 AM
Hibijibi
Thanks, I figured out it had to do with derivatives and was able to solve everything. I did miss the number line test though.. thanks!