Using the Mean Value Theorem, find a value of c that makes the conclusion true for
A) One or more hypotheses fail

Question

Using the Mean Value Theorem, find a value of c that makes the conclusion true for 
A) One or more hypotheses fail

Quizplus · Accepted Answer

Let f(x) = 11e^{x} - x^2 - 6x - 7. 
Since f(x) is continuous on [0,2] and differentiable on (0,2), by the Mean Value Theorem, there exists a value c in (0,2) such that

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

or

11e^c - 2c - 6 = (11e^{2} - 2(2) - 6)-(11e^{0} - 2(0) - 6)
 
Simplifying this equation gives

11e^c - 2c - 6 = 11e^2 -11,

and solving for c gives

c = ln(11(e^2 - 1) - 3).

Therefore, choice B is correct.

Using the Mean Value Theorem, Find a Value of C