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antjm
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let f(x,y) be a differentiable function.Given that fx(2,4) =-3 and fy(2,4) =8, find F(2,4) where u is in the same direction of a =<2,4>
Find F(2,4) of Differentiable Function
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In summary, the conversation discusses finding the value of F(2,4) for a differentiable function f(x,y) given fx(2,4) = -3, fy(2,4) = 8, and a vector a=<2,4>. The expert confirms that the gradient (F) is -3i + 8j, and suggests finding the dot product of the gradient with the unit vector of a to get the desired value. The student realizes that the unit vector would be different if a=<3,4>, and the expert agrees. The conversation ends with the expert praising the student's ability to solve the problem independently.
- #2
arildno
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You are very good at faithfully reproducing the QUESTION!
However, as you are well aware of when signing up here at PF, you have a duty to show what you have done so far.
However, as you are well aware of when signing up here at PF, you have a duty to show what you have done so far.
- #3
antjm
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I didn't know. here is what i have so far...
i know that the gradient (F) is -3i +8j
i think Duf(2,4) would be same
i think vector a = <3,4> to unit would be <3,4>/5
i know that the gradient (F) is -3i +8j
i think Duf(2,4) would be same
i think vector a = <3,4> to unit would be <3,4>/5
- #4
antjm
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i think i got it. grad (f) doted with unit
- #5
arildno
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antjm said:
That is correct!
Now, if your vector "a" was <2,4> as you wrote initially, that procedure is still the right one, but your unit vector would be somewhat different than if "a" was <3,4>.
Agreed?
- #6
antjm
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Agreed, a = <3,4> therefore magnitude would be 5 if a =<2,4> magnitude would be 2rt(5)
thanks
thanks
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arildno
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It was a pleasure!antjm said:
It is always great to meet a student like you who, when asked to do something on his own, suddenly hits upon the right procedure all by himself (as you did).
Then I know the student (in this case, you), have mastered the particular problem better than if I just had handed over the solution.
FAQ: Find F(2,4) of Differentiable Function
What is the definition of a differentiable function?
A differentiable function is a type of mathematical function that can be differentiated at every point in its domain. This means that the function is smooth and has a well-defined slope at every point.
How do you find the value of a differentiable function at a specific point?
To find the value of a differentiable function at a specific point, you can simply plug in the given value for the independent variable into the function and evaluate the resulting expression.
What is the significance of finding F(2,4) of a differentiable function?
F(2,4) represents the value of the differentiable function at the point (2,4) on the graph. This point is important because it helps to determine the behavior of the function and can be used to find the slope of the function at that point.
How do you graph a differentiable function?
To graph a differentiable function, you can use a graphing calculator or online graphing tool to plot the points and connect them to create a smooth curve. Alternatively, you can use the derivative of the function to find the slope at different points and plot the tangent lines to create the graph.
Can a function be differentiable at a point but not continuous?
No, a function cannot be differentiable at a point if it is not continuous at that point. This is because the definition of a differentiable function requires it to be continuous and smooth at every point in its domain.