Posting...#17

Last week in calculus we did not learn anything new. We took a practic ap monday and wensday then we went over it for tuesday and thursday.

Rolle's Theorem: Let f be continuous on a closed interval [a,b] and differentiable on the open interval (a,b) then there exsists a number c in (a,b) such that
f(b)-f(a)
f ' (c)=----------
b-a

Exampmle: F(x)=x^4 -2x^2 on [-2,2] find c f '(c)=0

Check if its continuous : YES
Check if its differentiable : YES

f(-2)=(-2)^4-2(-2)^2=8
F(2)=(2)^4-2(2)^2=8
f(-2)=f(2)

4x^3-4x=0
4x(x^2-1)=0
X=0,1,-1

Awnser C= -1,0,1

And thats it for roles theroem its pretty easy but for what im having trouble with is even easier so it would be great to get help.

I am confused on Critical Points so can some one explain how to do that for me.