Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function f(x)=x^2-3x +4, [0,3]

Question

anonymous · Answer

before we begin, since the function is a quadratic, the number you are looking for is smack in the middle, namely $1.5$

anonymous · Answer

you have to compute $f(0)$ and $f(3)$ did you do that?

anonymous · Answer

ok

anonymous · Answer

do u just plug in 0 and 3 into the equation?

anonymous · Answer

yes

anonymous · Answer

ok so I got 4 for the both of them when they were plugged in

anonymous · Answer

ok that means, since $f(0)=f(3)$ the conclusion of rolles is true

anonymous · Answer

which means the derivative of the function must be zero somewhere in the interval $(0,3)$

anonymous · Answer

take the derivative, set it equal to zero, and solve

anonymous · Answer

so the derivative is 2x-3 and when i solved it I got 3/2

anonymous · Answer

thank u sooo much!!