How do you find the critical numbers for cos(xx2+1) to determine the maximum and minimum?

1 Answer
Jul 30, 2016

So the critical point is x=0

Explanation:

y=cos(xx+1)
Critical point : It is the point where the first derivative zero or it does not exist.
First find the derivative , set it to 0 solve for x.
And we need to check is there a value of x which makes the first derivative undefined.

dydx=sin(xx+1).ddx(xx+1)( use chain rule of differentiation)

dydx=sin(xx+1)(1(x+1)x.1(x+1)2)Use product rule of differentiation.

dydx=sin(xx+1)(1(x+1)2)

Set dy/dx=0
sin(xx+1)(x+1)2=0
sin(xx+1)(x+1)2=0
sin(xx+1)=0xx+1=0,x=0

So the critical point is x=0