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Chapter 3: Q,17 (page 275)

For Exercises 15鈥�20, sketch the graph of a function f that has the indicated characteristics. If a graph is not possible, explain why.

f negative, f' positive, and f'' positive on [0,3].

Short Answer

Expert verified

The possible graph of f is the following.

Step by step solution

01

Step 1. Given information. 

The given interval is [0,3].

f is negative on interval.

f'is positive on the interval.

f'' is positive on interval.

02

Step 2. sign chart of function. 

Suppose both f and f' are differentiable on an interval I.

(a) If f'' is positive on I, then f is concave up on I.

(b) If f'' is negative on I, then f is concave down on I.

So sign chart of functions follows.

sign chart state that the f is decreasing on interval.

Information of f'' did not properly state the graph of f.

antiderivative of f' is in the form of f(x)+c.

so we will do a vertical shift of f.

03

Step 3. Possible graph of functions. 

The possible graph off''follows.

The possible graph of f follows.

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Most popular questions from this chapter

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=x3+3x2

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=cos3x-蟺2

Determine the graph of a function f from the graph of its derivative f'.

Find the possibility graph of its derivative f'.

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these.

f (x) = (x 鈭� 1.7) (x + 3)
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