Let f(1)= 1/t for t>0. For what value of t is f '(t) equal to the average rate of change on f on [a,b]
A) -sqrt(ab) B) sqrt(ab) C) -1/(sqrt[ab]) D) 1/(sqrt[ab])
E) sqrt [(1/2)(1/b-1/a)]
Please Help
I'm sure you meant $\displaystyle f(t) = \frac{1}{t}$
$\displaystyle f'(t) = -\frac{1}{t^2}$
$\displaystyle f'(t) = \frac{f(b) - f(a)}{b-a}$
$\displaystyle -\frac{1}{t^2} = \frac{\frac{1}{b} - \frac{1}{a}}{b - a}$
$\displaystyle -\frac{1}{t^2} = \frac{\frac{a-b}{ab}}{b - a}$
finish from here?