Question

Consider the function f(x) = x^3-3x^2+2x-18 on the interval [ 0 , 2 ]. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval:
f(x) is ___on[0,2]
f(x) is ___ on (0,2)
and f(0)=f(2)=____
then by rolle's theorem, there exists a c such that f'(c)=0.
c1=____ and c2=_____withc1<c2

Answer 1

It is continuous
derivative = 3x^2-6x+2 which is fine
f(0)=-18
f(2) = 8-12+4-18 = -18
find zeros of 3x^2-6x+2 = 0
(3-sqrt3)/3 and (3+sqrt3 )/3