Does the function #f(x) = 2x^2 − 5x + 1# satisfy the hypotheses of the Mean Value Theorem on the given interval [0,2]?

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Answer 1 · 2016-01-05T04:17:33

The Mean Value Theorem will be applicable since #f(x)# is differentiable on #(0,2)# and continuous on #[0,2]#.

The Mean Value Theorem states that there is some value #c# such that

#f'(c)=(f(2)-f(0))/(2-0)=(-1-1)/2=-1#

Since

#f'(x)=4x-5#,

find the value of #c# where:

#4c-1=-1#

#c=0#

This means that the tangent line at #x=0# has the same slope as the line connecting #(0,f(0))# and #(2,f(2))#.