Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Find the Difference Quotient

Find the difference quotient of f; that is, find

[f(x + h) - f(x)]/x, where h cannot be 0. Be sure to simplify.

Let rt = square root

f(x) = [sqrt{x + h} - rt{x})]/h

1. Is this the correct set up?

2. Must I rationalize the denominator in this example?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Find the Difference Quotient

No. That's good as it is.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Find the Difference Quotient

No. That's good as it is.

Bob

The fact that f(x) = rt{x} in the numerator indicates that I must rationalize the denominator or numerator in order to simplify.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Find the Difference Quotient

Only if the denominator contains a root.

B

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Find the Difference Quotient

Only if the denominator contains a root.

B

f(x) = [sqrt{x + h} - rt{x})]/h

f(x) = [sqrt{x + h} - rt{x})]/h • [sqrt{x + h} + rt{x})]/[sqrt{x + h} + rt{x})]

[sqrt{x + h} - rt{x})]/h • [sqrt{x + h} + r{x}]/[sqrt{x + h} + r{x}]

Numerator

[sqrt{x + h} - r{x}][sqrt{x + h} + r{x}] = h

Denominator

h[sqrt{x + h} + r{x}]

f(x) = h ÷    h[sqrt{x + h} + r{x}]

I know that h cancels out.

f(x) = 1/[sqrt{x + h} + r{x}]