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mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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) = -x^2 + 3x - 2 in terms of x and h. Be sure to simplify.

Let me see.

f(x) = [-(x + h)^2 + 3(x + h) - 2 -(-x^2 + 3x - 2)/h

f(x) = -(x^2 + 2xh + h^2) + 3x + 3h - 2 + x^2 - 3x + 2)/h

f(x) = (-x^2 - 2xh - h^2 + 3x + 3h - 2 + x^2 - 3x + 2)/h

f(x) = (-2xh - h^2 + 3h)/h

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

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Difference Quotient of f

Looks good.

B

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Children are not defined by school ...........The Fonz
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mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Difference Quotient of f

Looks good.

B

Looks like I totally get the process here. I don't know why Michael Sullivan decided to introduce a calculus topic this early in a college algebra textbook.