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#1 2024-03-28 11:15:08
- nycguitarguy
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- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 574
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?
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#2 2024-03-28 20:42:14
- Bob
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- Registered: 2010-06-20
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Re: Difference Quotient of f
Looks good.
B
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#3 2024-03-29 08:10:59
- nycguitarguy
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- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 574
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.
The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.
Dr. David Jeremiah
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