Question

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

Answer 1

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

Answer 2

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

Answer 3

ok

Answer 4

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

Answer 5

yes

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

thank u sooo much!!