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Chapter 4: Q7E (page 208)

Sketch the graph of a function that is continuous on [1, 5] and has the given properties.

7. Absolute minimum at 2, absolute maximum at 3, local minimum at 4.

Short Answer

Expert verified

The graph is sketched.

Step by step solution

01

Given data

The given function is the value of absolute minimum is at 2, absolute maximum is at 3, local minimum at 4.

02

Concept of Differentiation

Differentiation is a method of finding the derivative of a function. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables.

03

Sketch the graph

The graph of the given function is:

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Most popular questions from this chapter

Suppose \(f\) is an odd function and is differentiable everywhere. Prove that for every positive number b, there exists a number c in \(( - b\;,\;b)\) such that \({f^\prime }(c) = \frac{{f(b)}}{b}\).

Suppose f is a continuous function defined on a closed interval (a,b).

(a) What theorem guarantees the existence of an absolute maximum value and an absolute minimum value for \(f\)?

(b) What steps would you take to find those maximum and the minimum values?

If \({f^\prime }(x) = c\) (c a constant) for all x, use Corollary 7 to show that \(f(x) = cx + d\) for some constant d.

9–12 ■ Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers that satisfy the conclusion of the Mean Value Theorem.

11. \(f(x) = \ln x\), \((1\,,\;4)\)

A Norman window has a shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 30 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
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