Find F'(8) for F=f/[f-g], f(8)=5, f'(8)=1, g'(8)=3, g(8)=4

[help1234]

I have tried the following problems numerous times. This is a multiple choice homework, and the answers did not match up. It's gettin quite frustrating, so any help would be greatly appreciated!

For this one: it is Find F'(8) when F(x)= f(x)/[f(x)-g(x)] f(8)=5, f'(8)=1, g'(8)=3 g(8)=4

Honestly, I really just don't know what this means. I tried the quotient rule, but didn't work. There has to be something that I'm just missing..

Then theres this one: Find an equation for the tangent line to the graph of f(x)=7sinx(sin(x)) at the point P(pi, f(pi)).
The answer I keep getting is waaay off from the answer choices. :-/

If [x^(1/3)](x-2)^(2/3) for all x then the domain of f' is....

??

If the line 3x-4y=0 is tangent in the first quandrant to the curve y = x^3+ k then k is..

I got 1/2. But I'm not sure if it was right.

 

[stapel]

Find F'(8) when F(x)= f(x)/[f(x)-g(x)] f(8)=5, f'(8)=1, g'(8)=3 g(8)=4

Honestly, I really just don't know what this means.

This question is asking you to find the derivative of a function F(x), which is defined in terms of the (unstated) functions f(x) and g(x). You would need to use what you have learned about the Quotient Rule to find the symbolic expression for F'(x), and then you would need to plug the listed values into your expression, and simplify. :idea:

I tried the quotient rule, but didn't work.

Unfortunately, I am not able to help you find errors in work I cannot see. Sorry.

Find an equation for the tangent line to the graph of f(x)=7sinx(sin(x)) at the point P(pi, f(pi)).
The answer I keep getting is waaay off from the answer choices. :-/

What answer do you "keep getting"? How did you arrive at it?

If [x^(1/3)](x-2)^(2/3) for all x then the domain of f' is....

How does the function f(x) (or its derivative) relate to \(\displaystyle \sqrt[3]{x} \sqrt[3]{(x\, -\, 2)^2}\)? What is f(x)? :shock:

If the line 3x-4y=0 is tangent in the first quandrant to the curve y = x^3+ k then k is..

I got 1/2. But I'm not sure if it was right.

How did you arrive at your answer? When you compared the curves 3x - 4y = 0 and y = x[sup:2neeg3wx]3[/sup:2neeg3wx] + 1/2, what did you see? Why are you unsure of your solution?

Please be complete. Thank you!

Eliz.

 

[soroban]

Hello, help1234!

Exactly where is your difficulty?

\(\displaystyle \text{Given: }\:F(x) \:=\:\frac{f(x)}{f(x)-g(x)},\quad\begin{array}{ccc} f(8) \,= \,5 && f'(8) \,=\,1 \\ g(8)\,=\,4 && g'(8) \,=\,4 \end{array}\)
. . \(\displaystyle \text{Find:} \:F'(8)\)

I tried the quotient rule, but didn't work. . What didn't work ?

\(\displaystyle \text{Quotient Rule: }\;F'(x) \;=\;\frac{\left[f(x)-g(x)\right]\!\cdot\!f'(x) - f(x)\!\cdot\!\left[f'(x)-g'(x)\right]}{[f(x)-g(x)]^2}\)


\(\displaystyle \text{Then: }\;F'(8) \;=\;\frac{\left[f(8) - g(8)\right]\!\cdot\!f'(8) - f(8)\!\cdot\!\left[f'(8) - g'(8)\right]} {[f(8) - g(8)]^2}\)


Now plug in the given values and do the arithmetic . . .