Asked by Neeta
Verify the conditions for Rolle's Theorem for the function f(x)=x^2/(8x-15) 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 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.
Answers
Answered by
Steve
I 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.
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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.