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

• coookiemonste
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.

## 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.

?

## 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))

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.

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.

try using the fact that

$$log_a b^r=rlog_a b$$

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.