My Math Forum Derivative function - how do I insert values?

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 March 21st, 2009, 03:27 AM #1 Newbie   Joined: Mar 2008 Posts: 3 Thanks: 0 Derivative function - how do I insert values? Hi I have the derivative function: f'(x)= lim h->0 = [ f(x+h)-f(x) ] / h The question is: Find from the first principles the gradient of f(x) where f(x) is: a) x b) 5 c) x^3 My problem is, I have no idea how I insert these values into the formula...? If someone shows me how to do this step by step I would be very thankful!!
 March 21st, 2009, 05:19 AM #2 Guest   Joined: Posts: n/a Thanks: Re: Derivative function - how do I insert values? Plug in x+h for x in f(x+h). Like so. I will use x^3 $\lim_{h\to 0}\frac{\overbrace{(x+h)^{3}}^{\text{f(x+h)}}-\overbrace{x^{3}}^{\text{f(x)}}}{h}$ Expand: $\lim_{h\to 0}\frac{x^{3}+3hx^{2}+3xh^{2}+h^{3}-x^{3}}{h}$ Canceling the h's and leaving those that remain approach 0, leaves us with: $3x^{2}$, which is the derivative of $x^{3}$.
March 21st, 2009, 07:42 AM   #3
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 Originally Posted by toulouse f'(x)= lim h->0 = [ f(x+h)-f(x) ] / h Find from the first principles the gradient of f(x) where f(x) is: a) x b) 5 c) x^3 My problem is, I have no idea how I insert these values into the formula...?
Ouch! They were supposed to have covered that topic back in algebra!

To learn how, try studying some lessons on function notation.

Short version: Whatever they want you to evaluate at (like x, 5, or x^3), plug that in for every "x" in your function formula.

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