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Chapter 3: Q. 4 (page 286)

Explain why you can’t find the global maximum of a function f on an interval I just by finding all the local extrema of f and then checking to see which one has the highest value f(c)

Short Answer

Expert verified

The critical points of the function f won't help to locate any endpoints extrema because the derivative of the function may or may not be zero or fails to exist at the endpoints of the interval. The critical point is always calculated by equating the first derivative of the function equal to zero.

Step by step solution

01

Step 1. Given information.

We have to explain that why we can’t find the global maximum of a function f on an interval I just by finding all the local extrema of f and then checking to see which one has the highest value f(c)

02

Step 2. Explanation

The critical points of the function f won't help to locate any endpoints extrema because the derivative of the function may or may not be zero or fails to exist at the endpoints of the interval. The critical point is always calculated by equating the first derivative of the function equal to zero.

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Most popular questions from this chapter

Find the critical points of the function

f'(x)=1+x2-4

Find the possibility graph of its derivative f'.

For each set of sign charts in Exercises 53–62, sketch a possible graph of f.

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

ln(x2+1)

It took Alina half an hour to drive to the grocery store that is 20 miles from her house.

(a) Use the Mean Value Theorem to show that, at some point during her trip, Alina must have been traveling exactly 40 miles per hour.

(b) Why does what you have shown in part (a) make sense in real-world terms?
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