Apps of the Second Derivative

1. Determine where the function is concave upward and where it is concave downward.

(a) \(f(x)=-x^2+2x+2 \)  solution

(b) \(f(x)=4x^3-4x \)   solution

2. Find the inflection point, if it exists, of the function.   solution

\( \quad g(x)=4x^3-6x^2+8x-5 \)

3. Consider \( f(x)=2x^3-3x^2\). Answer the following using calculus.      solution

(a) Find the intervals on which \( f \) is concave up or down.

(b) Find the inflection points of \( f \).

4. Consider the function \( f(x)=x + x^2 - x^3\). Answer the following using calculus.  solution

(a) Find the intervals on which \(f\) is concave up or concave down.

(b) Find the \(x\)-coordinate(s) of inflection point(s) of \(f\).