Applications of Derivatives

Applications of Derivatives

Dr. G Garrido

Max and Min

Using Differentiation

Maximun and Minimum

 $f\left(x\right)=x^3-6x^2+7$  

• Determine f'(x)

• Determine f"(x)

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

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

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