   Chapter 10, Problem 16RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Given R   = 280 x  –  x 2 , find the absolute maximum and minimum for R when (a) 0 ≤ x ≤ 200 and (h) 0   ≤   x   ≤   100.

(a)

To determine

To calculate: The absolute maximum and minimum for the equation R=280xx2 when 0x200.

Explanation

Given Information:

The provided equation is R=280xx2 when 0x200.

Formula Used:

To obtain the critical points of a function,

Step 1. Find the first derivative of the function.

Step 2. Set the derivative equal to 0 now obtain the critical points.

For the function f is present, then the value f(a) is the absolute maximum of f

If f(a)f(x) for all x in the domain of f, absolute maximum is the highest point on the graph.

For the function f is present, then the value f(a) is the absolute minimum of f

If f(a)f(x) for all x in the domain of f, absolute minimum is the lowest point on the graph.

Calculation:

Consider the provided equation,

R=280xx2

Take out the first derivative of the above equation with respect to x by using the power rule,

R=2802x=2(140x)

Put the value of R=0,

2(140x)=0

Evaluate the values of x from the above equation:

2(140x)=0x=140

Hence, the value is x=140

(b)

To determine

To calculate: The absolute maximum and minimum for R for the expression R=280xx2 when 0x100.

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