# Thread: Concavity, and inflection points! Help!

1. ## 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.

2. 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.

Originally Posted by Hibijibi
b) Show that f must have exactly one inflection point.
Once again, solve for $\displaystyle f''(x)=0$

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?

3. 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!