Calculus
posted by Neeta on .
Verify the conditions for Rolle's Theorem for the function f(x)=x^2/(8x15) on the interval [3,5] and find c in this interval such that f'(c)=0
I verified that f(a)=f(b) and calculated f'(x)= (8x^2 30x)/64x^2 240x +225)
But I'm having trouble finding c when that derivative is equal to 0.

I find it a bit easier not to expand the derivative
f'(x) = 2x(4x15)/(8x15)^2
Clearly f'=0 when x is 0 or 15/4
So, f'(15/4)=0, and 3 < 15/4 < 5
f'(0)=0 also, but 0 is not in [3,5]
The graph at
http://www.wolframalpha.com/input/?i=x^2%2F%288x15%29+for+3+%3C%3D+x+%3C%3D+5
clearly shows that f'(3.75) is zero.