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January 30, 2015

January 30, 2015

Posted by **Neeta** on Tuesday, July 22, 2014 at 10:12pm.

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.

- Calculus -
**Steve**, Tuesday, July 22, 2014 at 11:26pmI find it a bit easier not to expand the derivative

f'(x) = 2x(4x-15)/(8x-15)^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%288x-15%29+for+3+%3C%3D+x+%3C%3D+5

clearly shows that f'(3.75) is zero.

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