Help with Test Q: What is fg'(3)?

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In summary, the conversation is about a question from a test that the person is unsure about and is seeking help to find the answer. They provide the given values for f(3), g(3), f'(3), and g'(3) and the answer choices for fg'(3). They also mention a homework help forum and ask for assistance in finding the correct answer.
  • #1
JoshuaC
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Hello!

I have a question from a test that I wasn't sure about, so I guessed.

The question is:

f(3)= 5
g(3)= -4
f'(3)= 1.1
g'(3)= .7

What is fg'(3)

Answer choices: a) .9 b) .4 c) -.9 d) -.4

Does anyone know the answer? And how did you get it?

Help would be much appreciated. Thanks!
 
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  • #2
Do you mean (fg)'(3)?

Also, homework help forum.

Also (fg)'=fg'+gf'
So just plug in what they gave.
 
  • #3
JoshuaC said:
Hello!

I have a question from a test that I wasn't sure about, so I guessed.

The question is:

f(3)= 5
g(3)= -4
f'(3)= 1.1
g'(3)= .7

What is fg'(3)

Answer choices: a) .9 b) .4 c) -.9 d) -.4

Does anyone know the answer? And how did you get it?

Help would be much appreciated. Thanks!

You are required to show some effort at answering the question when posting schoolwork questions. Please use the hints from johnqwertyful and show your work...
 

What is fg'(3)?

1. What does fg'(3) represent?

fg'(3) represents the derivative of the function fg at the point 3. This means it is the slope of the tangent line to the curve at the point (3, fg(3)).

2. How do I calculate fg'(3)?

To calculate fg'(3), you will need to use the chain rule. First, find the derivative of f at 3, then multiply it by the derivative of g at f(3).

3. Can I use a calculator to find fg'(3)?

Yes, most scientific calculators have a built-in derivative function that you can use to find fg'(3). Make sure to follow the correct syntax for entering the function.

4. What is the significance of fg'(3)?

fg'(3) is important because it tells us the rate of change of the function fg at the specific point 3. This can help us understand the behavior of the function and make predictions about its values at nearby points.

5. How can I use fg'(3) in real-life situations?

fg'(3) can be used in various real-life situations, such as in physics to calculate velocity or acceleration, in economics to analyze marginal costs, or in engineering to optimize designs. It can also be used to solve optimization problems and find the maximum or minimum values of a function.

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