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Chapter 2: Q. 28 (page 166)

Sketch a graph of the associated slope function ffor each functionf in Exercises 25–30.

Short Answer

Expert verified

The graph of the function is:

Step by step solution

Step 1. Given Information.

The graph of the function.

Step 2. Draw the tangent line

Draw the tangent lines at few points as follows:

Step 3. Draw the associated function.

From the above graph, the tangent line at any point of the curve has positive, negative and zero slopes.

So the graph of the slope function is:

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Most popular questions from this chapter

Use (a) the $h \to 0$ definition of the derivative and then

(b) the $z \to c$ definition of the derivative to find $f' (c)$ for each function f and value $x = c$ in Exercises 23–38.

28. $f (x) = x^{4} + 1, x = 2$

A tomato plant given $x$ ounces of fertilizer will successfully bear $T (x)$ pounds of tomatoes in a growing season.

(a) In real-world terms, what does $T (5)$ represent and what are its units? What does $T' (5)$ represent and what are its units?

(b) A study has shown that this fertilizer encourages tomato production when less than $20$ ounces are used, but inhibits production when more than $20$ ounces are used. When is $T (x)$ positive and when is $T (x)$ negative? When is $T' (x)$ positive and when is $T' (x)$ negative?

For each function $f (x)$ and interval localid="1648297458718" $[a, b]$ in Exercises localid="1648297462718" $81 - 86$ , use the Intermediate Value Theorem to argue that the function must have at least one real root on localid="1648297466951" $[a, b]$ . Then apply Newton’s method to approximate that root.

localid="1648297471865" $f (x) = x^{3} - 3 x + 1, [a, b] = [1, 2]$

For each function $f (x)$ and interval $[a, b]$ in Exercises $81 - 86$ , use the Intermediate Value Theorem to argue that the function must have at least one real root on $[a, b]$ . Then apply Newton’s method to approximate that root.

localid="1648369345806" $f (x) = x^{4} - 2, [a, b] = [1, 2]$ .

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

role="math" localid="1648290170541" $f (x) = \frac{x - 1}{x + 3}$

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Sketch a graph of the associated slope function ffor each functionf in Exercises 25–30.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Draw the tangent line

Step 3. Draw the associated function.

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Most popular questions from this chapter

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