MHB Find the Slope of a Curve y=f(x) at (a,f(a)) - Determine a f

[Teh]

The limit below represents the slope of a curve y=​f(x) at the point​ (a,f(a)). Determine a​ f

View attachment 6113After finding the f(x) and a, I did this:8(3^2+3h(3)+3h(3)+h^2)-72 dividing by h

getting h(8h^2+144) dividing by h; canceling the h's

and the plugging in the limit h --> 0 getting 144. But I am getting it wrong.

What is the issue?

 

[MarkFL]

Re: The limit below represents the slope of a curve y=​f(x) at the point​ (a,f(a)). Determine a​ f

$$\frac{8(3+h)^2-72}{h}=\frac{8(9+6h+h^2-9)}{h}=\frac{8h(6+h)}{h}=8(6+h)$$

Then as $h\to0$, the limit is 48. :)

 

[Teh]

Re: The limit below represents the slope of a curve y=​f(x) at the point​ (a,f(a)). Determine a​ f

$$\frac{8(3+h)^2-72}{h}=\frac{8(9+6h+h^2-9)}{h}=\frac{8h(6+h)}{h}=8(6+h)$$

Then as $h\to0$, the limit is 48. :)

What! cmon...ahhhh okay dang it need more math pratice XD...what happen to 72?