Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 5.1, Problem 19E

To determine

To find: theextreme values of the function and where they occur.

Expert Solution & Answer

Answer to Problem 19E

the minimum value is 1 at x=2 .

Explanation of Solution

Given information:

The function is y=2x2−8x+9

Calculation: the function is defined for each value of x, the domain of the function has no endpoints so all the extreme values must occur at critical points,

To find the extreme values of function, first find its derivative,

y=2x2−8x+9y'=4x−8 [differentiate and simplify]

For critical points equal the derivative of function to zero,

4x−8=0x=2 [simplify]

Now substitute in function,

y=2x2−8x+9y=2(2)2−8(2)+9 [substitute x=2 ]y=8−16+9 [square and multiply]y=1 [simplify]

Thus, the minimum value is 1 at x=2 .

Chapter 5.1, Problem 18E

Chapter 5.1, Problem 20E

Chapter 5 Solutions

Calculus: Graphical, Numerical, Algebraic

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