Solve for a and b: Find f'(10) and Simplify Quotient

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The discussion focuses on simplifying the expression f(10 + h)/h - f(10)/h for the function f(x) = 8x^2 - 7x + 5, ultimately leading to a form of ah + b. Participants express confusion about the problem's requirements and the application of derivatives, with one suggesting that the derivative could be directly evaluated at x=10 for the slope of the tangent line. There is a light-hearted exchange about identities and a request for help with differentiation rules, particularly for a new problem involving multiple x variables. The conversation highlights the challenges faced by learners in understanding calculus concepts and applying algebraic simplifications. Overall, the thread emphasizes the importance of grasping foundational calculus principles for solving related problems.
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Let f(x) = 8x^2 -7x +5. Then the quotient f(10 + h)/h - f(10)/h can be simplified to ah + b when a = ? and b = ?

I'm completely stumped on this one...I'm not even sure what they're asking!

Is it saying that when x=10, the rate of change is given by the function ah + b?

If so, why can't i just plug in the 10 into the derivative 16x -7 to find the slope of the tangeant line and find the equation that way ?
 
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They'r asking you to do that,no calculus involved whatsoever,just simple algebra
\frac{8(10+h)^{2}-7(10+h)+5-8(10)^{2}+7(10)-5}{h}

Daniel.
 
OHHHHHH

I tried that but forgot to inverse the symbols within f(x) brackets...haha :blushing:

That was helpful...are you daniel jackson of stargate?
 
Nope,i'm the one & only Daniel Ciobotu from Craiova/Romania... :smile:

Daniel.
 
Might as well continue this thread with some more newbie questions

I'm trying my hand at some harder stuff that's not part of my homework.

How would I find the derivative of 5x + 3*sqrt of x ? There are two x variables so 2 h differences for each?
 
Do you know the rules of differentiation??E.g.
(x^{n})'=...?

Daniel.

P.S."n" is real...
 
n * x^n-1 ?

That's about all i know ;D
 
Well,that's good enough.Apply that formula for your case.

Daniel.
 
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