Applications of Derivatives Lesson Slides: 6 Slides

6 Slides • 0 Questions

1

Applications of Derivatives

Dr. G Garrido

2

Max and Min

Using Differentiation

3

Maximun and Minimum

f\left(x\right)=x^3-6x^2+7

Determine f'(x)
Determine f"(x)

4

$f"\left(0\right)<0\ Max$ $f'\left(x\right)=3x^2-12x=0\ then\ x=0\ x=4$ $f"\left(x\right)=6x-12$
$f"\left(4\right)\ >\ 0\ \ Min$
$f"\left(0\right)\ <0\ Max$

5

Determine Min or Max
$f\left(x\right)=x^2+2x+3$

$f'\left(x\right)=2x+2=0\$
x=-1
f"(-1)=2 >0 then It is Min

6

Determine Min or Max

$f\left(x\right)=-x^2+3x_{ }-1$

f'\left(x\right)=-2x+3

=0

x=3/2

f"(x) =-2 <0 then It is Max

Applications of Derivatives

Dr. G Garrido

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