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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

01

Step 1. Given Information.

The graph of the function.

02

Step 2. Draw the tangent line

Draw the tangent lines at few points as follows:

03

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

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)=xx+1-2

Velocity v(t) is the derivative of position s(t). It is also true that acceleration a(t) (the rate of change of velocity) is the derivative of velocity. If a race car’s position in miles t hours after the start of a race is given by the function s(t), what are the units of s(1.2)? What are the units and real-world interpretation of v(1.2)? What are the units and real-world interpretations of a(1.2)?

For each function fgraphed in Exercises 65-68, determine the values of xat which ffails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.

For each function graphed in Exercises 65-68, determine the values of xat which ffails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.

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)=x(3x2+1)9
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