Question #3fe4c

2 Answers
Dec 16, 2017

#c=4#

Explanation:

#f'(x) = -16+4x = 0# at #x=4#

#f# is continuous and differentiable everywhere because it is a polynomial.

#f(3) = 29 = f(5)# so the hypotheses are satisfied.

Dec 16, 2017

#c=4#

Explanation:

First, state that all quadratic functions are everywhere continuous and differentiable.

Next, solve for f(3) and f(5); they have to be equal.

#f(3)=1-16(3)+2(3)^2=-29#

#f(5)=1-16(5)+2(5)^2=-29#

Therefore, Rolle's Theorem applies.

To find the value(s) of #c# that the problem is asking for, find the first derivative of the function:

#f#'#(x)=-16+4x#

From this, solve for #x# where #f#'#(x)# equals #0# on the interval [3,5].

#4x=16#
#x=4#

Therefore #c=4#