Question

rolles theorem ...can someone help me with problem 1 and go over with me with the steps

http://www.analyzemath.com/calculus/MeanValueTheorem/mean_val_theorem.problems.html

Answer 1

@ganeshie8 @zepdrix

Answer 2

\[\large\rm f(x)=-2x^3+6x-2,\qquad\qquad\qquad x\in\left[-2,2\right]\]

Answer 3

This is a polynomial,
so we have continuity and differentiability,
good good good. All of the requirements for MVT are met.

Answer 4

So MVT guarantees that we'll have at least one tangent line with slope equal to that of the secant line connecting the end points of the interval.

Answer 5

it doesn't matter what the function looks like...
MTV guarantees we will find at least one tangent line with the same slope as the secant line (so they will be parallel as illustrated in this picture example).