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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) = 1/x^2 in terms of x and h. Be sure to simplify.
Let me see.
f(x) = [1/(x + h)^2 - (1/x^2)]/h
f(x) = [1/(x^2 + 2xh + h^2) - (1/x^2)]/h
After further simplifying, I got the following answer:
f(x) = (2x - h)/[(x^2)(x^2 + 2xh + h^2)]
You say?
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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f(x) = (2x - h)/[(x^2)(x^2 + 2xh + h^2)]
Somewhere in that simplification you have lost a minus sign. It should be
f'(x) = (-2x - h)/[(x^2)(x^2 + 2xh + h^2)]
Then when h tends to zero it becomes f'(x) = (-2x )/[(x^2)(x^2)] = -2/x^3
Other minor point. Don't start with the secant function as f(x). f(x) is the original function not the secant function. I've used f'(x) as this is a common notation for the differential function.
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
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f(x) = (2x - h)/[(x^2)(x^2 + 2xh + h^2)]
Somewhere in that simplification you have lost a minus sign. It should be
f'(x) = (-2x - h)/[(x^2)(x^2 + 2xh + h^2)]
Then when h tends to zero it becomes f'(x) = (-2x )/[(x^2)(x^2)] = -2/x^3
Other minor point. Don't start with the secant function as f(x). f(x) is the original function not the secant function. I've used f'(x) as this is a common notation for the differential function.
Bob
Ok. Thanks for letting me know.
Now, does f '(x) mean f prime of x?
Is f prime of x the slope which is the derivative?
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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yes.
There's two notations used but they mean the same f'(x) = dy/dx
Note. If you had z = f(x) then it would be dz/dx
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
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yes.
There's two notations used but they mean the same f'(x) = dy/dx
Note. If you had z = f(x) then it would be dz/dx
Bob
I can say dy/dx reads d y d x. YES?
If I have w = f(x), I can then say dw/dx. YES?
If I had f(z), the derivative is f prime of z. Yes?
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
Offline
In the UK folk usually say d y by d x . Your other statements are correct.
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
Offline
In the UK folk usually say d y by d x . Your other statements are correct.
Bob
Glad to know my statements are correct.
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
Offline
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