please show your work Consider the function fr rs 3r2 2r 17

please show your work.

Consider the function f(r) rs 3r2 2r 17 on the interval 0, 2. verify that this function satisfies the three hypotheses of Rolle\'s Theorem on the inverval: f(r) is on 0, 2 f(r) is on (0,2) and f (0 f(2) Then by Rolle\'s theorem, there exists a C such that f\'(c) 0. Find the values c that satisfy the conclusion of Rolle\'s theorem and Co with C1 c2.

Solution

f(0)=-17

f(2)=-17

3c^2-6c+2=0

c=6+sqrt(36-24)/6=1+-(1/sqrt(3))