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Chapter 2: Q. 31 (page 166)

Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

Short Answer

Expert verified

The graph is:

Step by step solution

Step 1. Given Information

We are given the associated slope function f' for some unknown function f and we need to sketch a possible graph of f.

Step 2. Finding the graph

The function increases from $- 2 < x < 0$ and decreases for $x < - 2$ and $x > 0$ .

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Most popular questions from this chapter

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

$f (x) = \frac{1}{\sqrt{x^{2} + 1}}$

Use the definition of the derivative to find $f'$ for each function f in Exercises 39-54

$f (x) = - x^{3} - x + 1$

Prove that if f is any cubic polynomial function $f (x) = a x^{3} + b x^{2} + c x + d$ then the coefficients of f are completely determined by the values of f(x) and its derivative at x=0 as follows

$a = \frac{f "' (0)}{6}; b = \frac{f " (0)}{2}; c = f' (0); d = f (0)$

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

$f (x) = \sqrt{2 - \sqrt{3 x + 1}}$

Suppose h(t) represents the average height, in feet, of a person who is t years old.

(a) In real-world terms, what does h(12) represent and what are its units? What does h' (12) represent, and what are its units?

(b) Is h(12) positive or negative, and why? Is h'(12) positive or negative, and why?

(c) At approximately what value of t would h(t) have a maximum, and why? At approximately what value of t would h' (t) have a maximum, and why?

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Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the graph

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Most popular questions from this chapter

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