Question

Please Help! Calculus!

determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s Theorem can be applied, find all values of c in the open interval (a,b) such that f'(c)=0.

1. f(x)=x^2-5x+4 [1,4]
2. f(x)= cos x, [0,2pi]

Answer 1

@SolomonZelman

Answer 2

for the first f(1)=f(4) and f is contiunuos in [1,4] then you can apply the rolle theorem
there is an c in ]1,4[| f'(c)=0

Answer 3

continuos and differenciable

Answer 4

same for the second f(0)=f(2*pi)....