Question

I have 1-3 right, I can provide them if anyone wants, I'm just stuck on the 4th, my math isn't leading anywhere =/

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.
f(x) = -1/8 x^2
Step 1: f(x + h) =
Step 2: f(x + h) - f(x) =
Step 3: (f(x + h) - f(x))/h =
Step 4: f'(x) = lim(h->0): (f(x + h) - f(x))/h =

Answer 1

"four-step process"? Wow!

Have you considered writing the actual expressions of the functions, rather than their symbolic expressions?

Rather than "f(x)", write "-1/8 x^2"
Rather than "f(x+h)", write "-1/8 (x+h)^2"

Then, work a little algebra to simplify the resulting total expression.

Answer 2

Yes, I did the first three, but I'm having problems with my algebra on the fourth, is my question really that stupid?? I feel embarrassed now =/
1) -1/8(x+h)^2
2)(-1/8(x+h)^2)-(-1/8x^2)
3)((-1/8(x+h)^2)-(-1/8x^2))/2

Answer 3

Where did "/2" come from? Should be "/h".

Clarify. Is it \(f(x) = -\dfrac{1}{8x^{2}}\;or\;f(x) = -\dfrac{1}{8}x^{2}\)

Answer 4

Ah yes, typo that's an h not 2 my bad. And it's the second one

Answer 5

Okay, expand: \(-\dfrac{1}{8}\left((x-h)^{2} - x^{2}\right)\)

Answer 6

BTW - Do you have a textbook with this method in it? If so, will you tell me exactly what textbook it is?