## The Second Derivative and the Shape of a Function f(x)

Read this section to learn how the second derivative is used to determine the shape of functions. Work through practice problems 1-9.

### Practice Answers

**Practice 1:** See Fig. 6.

**Fig. 6**

so is concave down at the critical value so is a rel. max.

so is concave up at the critical value so is a rel. min.

**Fig. 18**

**Practice 3:** The points labeled and in Fig. 8 are inflection points.

**Practice 4: **

The only candidates to be Inflection Points are and .

If , then (neg)(neg) is positive.

If , then (pos )(neg) is negative.

If , then
(pos)(pos) is positive.

changes concavity at and so **and** **are Inflection Points**.

**Fig. 19**