# Math Help - Secant Line Slope Formula

1. ## Secant Line Slope Formula

Im stuck on this problem and don't know what to do.

Using the formula for the slope of a secant line passing through two points on a curve f(x+h)-f(x)/h determine this secant line slope formula for the function f(x)=3x^2-5x. Yu must simplify your result algebraically.

2. Originally Posted by oregon88
Im stuck on this problem and don't know what to do.

Using the formula for the slope of a secant line passing through two points on a curve f(x+h)-f(x)/h determine this secant line slope formula for the function f(x)=3x^2-5x. Yu must simplify your result algebraically.
Just plug it in?

For example, if f(x) = 93x, and if you want f(x+h), you will write f(x+h) = 93(x+h).

3. So I would do (3x^2-5x)(x+h)-(3x^2-5x)(x)/h?

4. Originally Posted by oregon88
So I would do (3x^2-5x)(x+h)-(3x^2-5x)(x)/h?
Hmm, not so much, look at this

g(x) = 2x^2

g(5) = 2(5)^2

g(x+a) = 2(x+a)^2

you replace every "x" on the right hand side with whatever's in parentheses after the g on the left hand side.. make sense?

Edit: changed from letter f to letter g to avoid potential confusion.

5. so then it would be f((3x^2-5x)+h)-f(3x^2-5x)/h?

6. Originally Posted by oregon88
so then it would be f((3x^2-5x)+h)-f(3x^2-5x)/h?
Ok, write

f(x) = 3x^2-5x

f(x+h) = ?

Now think of x+h as a single number (because that's what it is). So you understand that

f(7) = 3(7)^2-5(7) right?

Now using the same method, try to replace the question mark below with the appropriate expression

f(x+h) = ?

7. Ok, write

f(x) = 3x^2-5x

f(x+h) = ?

Now think of x+h as a single number (because that's what it is). So you understand that

f(7) = 3(7)^2-5(7) right?

Now using the same method, try to replace the question mark below with the appropriate expression

f(x+h) = 3(x+h)^2 - 5(x+h)

So whould I continue and do f(x+h) - f(x)/h and get 6x + 3h -5 in the end?

8. Originally Posted by oregon88
f(x+h) = 3(x+h)^2 - 5(x+h)
This is good.

Originally Posted by oregon88
So whould I continue and do f(x+h) - f(x)/h and get 6x + 3h -5 in the end?
Yes, I also get this. Good job!

By the way, it really is better practice to write parentheses, like this:

(f(x+h) - f(x))/h

This way respects the standard order of operations.

9. ## Difference quotient

The big butt-kicker about diff quotient problems is sign errors, so be on your toes! My solution is attached. Sorry, not too great at latex yet.

Be Well,
T