Slope of secant line in terms of x&h

Question

Slope of secant line in terms of x&h of f(x)=1/x

I have no idea what in terms of x & h means.

I found this formula

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

But I don't know to apply it to this problem.

Any help is appreciated, thank you.

Answer 1

Hi Elizabeth,

f(x+h) means that we replace x with (x+h) in the function.

Since f(x) = 1/x, then f(x+h) = 1/(x+h)

Now we have all we need to insert into the secant line slope formula that you’d found:

[f(x+h) - f(x)] / h is the original formula you had found.

Replace f(x+h) with 1/(x+h), and replace f(x) with 1/x to get one big fraction:

[1/(x+h) - 1/x] / h

Focusing just on the numerator first, we have 1/(x+h) - 1/x. The common denominator of these two fractions is (x+h)*x so once we adjust each fraction then we can subtract them and get:

[x - (x+h)]/[(x+h)*x]

= -h/[(x+h)*x]

Remember that this is the numerator of the big fraction. We also had a denominator of h, meaning that we can now divide the numerator by h and get:

-1/[(x+h)*x]

Please let me know if I can be more helpful, thanks!

Joe