Solving CALC AB Problems for f'(2)=3

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In summary, the conversation discusses finding the value of k in the function f(x)=ln(3x+2)^k, given that f'(2)=3. The attempted solution involves taking the derivative and plugging in the given values, but the resulting answer of k=8 does not match the given answer. Further discussion includes using the property log_a b^r=rlog_a b to potentially find the correct value of k without using a calculator.
  • #1

Homework Statement


Let f be the functions f(x)=ln(3x+2)^k for some positibe constant k.
If f'(2)=3, what is the value of k?
the answer is 8,but i don't think i am taking the derivative right.



Homework Equations


?


The Attempt at a Solution


f'(x)=3k*ln(3x+2)^(k-1)/(3x+2)
then i plugged in (2,3) into the derivative above.
and i got k=8/(ln8)(8^(k-1))
 
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  • #2
The derivative is correct, but the answer is not 8. If you plug in (2,3) into your derivative with k=8, you will get a contradiction.
 
  • #3
my ap book says the answer is 8, however it may be wrong.
but how would you find the value of k?
i am not allowed to use a calculator with this problem.
 
  • #4
try using the fact that

[tex]log_a b^r=rlog_a b[/tex]
 
  • #5
AH!
thank you!
 

1. How do you solve for f'(2) in a CALC AB problem?

To solve for f'(2), you will need to take the derivative of the given function f(x) and then plug in x=2. This will give you the value of the derivative f'(2) at that specific point.

2. What is the significance of f'(2)=3 in a CALC AB problem?

f'(2)=3 represents the slope of the tangent line at x=2. This means that at x=2, the rate of change of the function f(x) is 3. It is an important value to calculate in order to understand the behavior of the function at that point.

3. Can you use the Power Rule to solve for f'(2) in a CALC AB problem?

Yes, you can use the Power Rule to find the derivative of a polynomial function and then plug in x=2 to calculate f'(2). However, for more complicated functions, you may need to use other derivative rules such as the Chain Rule or Product Rule.

4. How can you check if your solution for f'(2) is correct in a CALC AB problem?

You can check your solution by taking the derivative of the given function and then plugging in x=2 to see if you get the same value. Additionally, you can graph the function and its derivative on a graphing calculator to visually compare the values at x=2.

5. Is f'(2) always a constant value in a CALC AB problem?

No, f'(2) can vary depending on the function and the given point x=2. It is only a constant value if the function is linear or if it has a constant rate of change at x=2.

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