# Local maxima and Local minima ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2, Problem 71RE
To determine

## To calculate: Local maxima and Local minima

Expert Solution

Max =350 at x=046

Min =203 at x=046

### Explanation of Solution

Given information:

33+16x25x3=f(x)f(x)=25x3+16x+33

Calculation:

Local maxima and local minima For finding max and min

f'(x)=0

Therefore

3(25)x2+16=0x2=1675=163×25=±453x=±453x=±046

Now, you have to check for which value it max and for which value is min.

So you have to take double derivative

f"(x)=6(25x)

On substituting +046

You get

f"(x)=+6×25×046>0

Hence 046 gives minima

Therefore +046 gives maxima

Sub 046 to get maximum values you have to substitute in f(x) therefore

25(046)2+16(046)+33=3507     (Maxima)

Sub 046

25(046)2+16(046)+33=2035

Maxima 350 at x=046

Minima =203 at x=046

Equation of hyperbola with center (h,k) is given

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