Simplifying [f(10+h)-f(10)]/h for f(x)=8x²-7x+5

[speed racer 5]

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 ?

 

[dextercioby]

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.

 

[speed racer 5]

OHHHHHH

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

That was helpful...are you daniel jackson of stargate?

 

[dextercioby]

Nope,i'm the one & only Daniel Ciobotu from Craiova/Romania...

Daniel.

 

[speed racer 5]

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?

 

[dextercioby]

Do you know the rules of differentiation??E.g.
$$(x^{n})'=...?$$

Daniel.

P.S."n" is real...

 

[speed racer 5]

n * x^n-1 ?

That's about all i know ;D

 

[dextercioby]

Well,that's good enough.Apply that formula for your case.

Daniel.