F(x)=ln(x-3) [4,6]?

Question

Find the value or values of c that satisfy the equation
f(b)−f(a)/
b−a

 

a. 5.820
b.4.820
c.5.885
d.+-4.820

Answer 1

f(x) = ln(x-3) is continuous on [4,6] and differentiable on (4,6).

 

By the Mean Value Theorem, there is at least one number, c, in the interval (4,6) so that f'(c) = [f(6) - f(4)]/(6-4)

 

                             1/(c-3) = [ln3 - ln1]/[3-1]

 

                             1/(c-3) = 0.5493

 

                                c-3 = 1.82

 

                                   c = 4.82