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nycguitarguy

Member

Registered: 2024-02-24

Posts: 523

Difference Quotient of f

The slope of the secant line containing the two points
(x, f(x)) and (x + h, f(x + h)) on the graph of a function y = f(x) may be given as

m_sec = [f(x + h) - f(x)]/[(x + h) - x] which leads to [f(x + h) - f(x)]/h, where h cannot = 0.

Express the slope of the secant line for the function f(x) = 2x^2 + x in terms of x and h. Be sure to simplify.

Let me see.

f(x) = [2(x + h)^2 + (x + h) - (2x^2 + x)]/h

f(x) = (2(x^2 + 2xh + h^2 + x + h - 2x^2 - x)/h

f(x) = (2x^2 + 4xh + 2h^2 + x + h - 2x^2 - x)/h

f(x) = (4xh + 2h^2 + h)/h

f(x) = 4x + 2h

f(x) = 2(2x + h)

Correct?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,184

Re: Difference Quotient of f

f(x) = (4xh + 2h^2 + h)/h

f(x) = 4x + 2h

f(x) = 2(2x + h)

When you divide by h there should be an h/h = 1 term

Bob

---

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: 523

Re: Difference Quotient of f

f(x) = (4xh + 2h^2 + h)/h

f(x) = 4x + 2h

f(x) = 2(2x + h)

When you divide by h there should be an h/h = 1 term

Bob

f(x) = (4xh + 2h^2 + h)/h

f(x) = 4x + 2h + 1

f(x) = 2(2x + h) + 1

Yes?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,184

Re: Difference Quotient of f

That's it.

Bob

---

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: 523

Re: Difference Quotient of f

That's it.

Bob

Thank you, Bob. Some knucklehead asked if my question is homework.
Please, read my reply.