1. ## Brief Calculus Help

Hello,
I am new here. I am taking an online calculus course and I am having trouble answering these two questions:

Find and simplify.

f (x)=7x-1

A) f (x+h)-f (x) /h Bold is on top of h

f (x)=4-x^2

A) f (x+h)-f (x) /h Bold is on top of h

B) f (x+h)-f (x)

Thank You

2. Originally Posted by bwirth
Hello,
I am new here. I am taking an online calculus course and I am having trouble answering these two questions:

Find and simplify.

f (x)=7x-1

A) f (x+h)-f (x) /4 Bold is on top of 4

f (x)=4-x^2

A) f (x+h)-f (x) /4 Bold is on top of 4

B) f (x+h)-f (x)

Thank You
Function notation means you evaluate the function f at the value given

$\displaystyle \displaystyle \frac{[f(x+h)-f(x)}{4}=\frac{[7(x+h)-1]-(7x-1)}{4}$

3. Here's a kick start.

$\displaystyle \displaystyle \frac{f(x+h)-f(x)}{4} = \frac{(7(x+h)-1)-(7x-1)}{4}= \frac{7x+7h-1-7x+1}{4}$

4. Thanks Pickslides,

That helps me understand how to do that type of problem. I seem to be doing something wrong with the ^2 problems though. By the way, I changed the equation above, they are over h not 4.

5. I had a feeling h would be in the denominator

$\displaystyle \displaystyle \frac{f(x+h)-f(x)}{h} = \frac{(4-(x+h)^2-1)-(4-x^2)}{h}= \frac{4-(x^2+2xh+h^2)-4+x^2}{h}=$ $\displaystyle \displaystyle\frac{4-x^2-2xh-h^2-4+x^2}{h}= \frac{-2xh-h^2}{h}= \frac{h(-2x-h)}{h} = -2x-h$

6. Originally Posted by pickslides
I had a feeling h would be in the denominator

$\displaystyle \displaystyle \frac{f(x+h)-f(x)}{h} = \frac{(4-(x+h)^2-1)-(4-x^2)}{h}= \frac{4-(x^2+2xh+h^2)-4+x^2}{h}=$ $\displaystyle \displaystyle\frac{4-x^2-2xh-h^2-4+x^2}{h}= \frac{-2xh-h^2}{h}= \frac{h(-2x-h)}{h} = -2x-h$
Your the man Pickslides. That helped me figure out the rest of my homework problems. I really wish these online classes followed along with a book. Thanks again!