- #1
tachyon_man
- 50
- 0
Question: Show that the derivative of f(x) = (x-a)m (x-b)n vanishes at some point between a and b if m and n are positive integers.
My attempt:
f(x) = (x-a)m (x-b)n
f '(x) = m(x-a)m-1 (x-b)n + n(x-a)m (x-b)n-1
f '(x) = [(x-a)n-1 (x-b)n-1 ] [(m)(x-b) +(n)(x-a)]
And this is as far as I got.
My attempt:
f(x) = (x-a)m (x-b)n
f '(x) = m(x-a)m-1 (x-b)n + n(x-a)m (x-b)n-1
f '(x) = [(x-a)n-1 (x-b)n-1 ] [(m)(x-b) +(n)(x-a)]
And this is as far as I got.