chapter 9: Application of Differentiation

 $M_T=f'\left(x\right)=\frac{dy}{dx}$  

 $M_N=-\frac{1}{M_T}$  

Equation  $y-y_1=m\left(x-x_1\right)$  

 $f'\left(x\right)=\frac{dy}{dx}=0$  to find stationary point(s)

2 method to find the nature of stationary points ( first derivative and second derivative)

 $f''\left(x\right)>0\$  minimum point

 $f''\left(x\right)<0$  maximum point

 $f''\left(x\right)=0$  (test failed ) back to first derivative test)

 $\overline{C\left(x\right)}=\frac{C\left(x\right)}{x}$  (Average Cost) 

 $R\left(x\right)=p\left(x\right).x$  

 $\pi\left(x\right)=R\left(x\right)-C\left(x\right)$