# Thread: Help with a calculus test question

1. ## Help with a calculus test question

I need to redo this question to get partial credit but it looks like none of the examples or homework we've done:

Given $\displaystyle f'(x) = 4e^(2x)$ and$\displaystyle f(0) = 1$, find the function $\displaystyle f(x)$?

2. Let's see it this way, if you have $\displaystyle f(x)=C\cdot{x^2}+k$ where C and k are real numbers, derivating: $\displaystyle f'(x)=C\cdot{2}\cdot{x}$

Then $\displaystyle C\cdot{x^2}+k$ is the anti-derivative of $\displaystyle C\cdot{2}\cdot{x}$

That's denoted as follows: $\displaystyle \int{C\cdot{2}\cdot{x}}\cdot{dx}=C\cdot{x^2}+k$

To find the anti-derivative you need (there are an infinit number of them) you have to find the constant k, and for that you use the other information you have

http://www.mathhelpforum.com/math-he...66-post12.html

3. Originally Posted by PaulRS
Let's see it this way, if you have $\displaystyle f(x)=C\cdot{x^2}+k$ where C and k are real numbers, derivating: $\displaystyle f'(x)=C\cdot{2}\cdot{x}$

Then $\displaystyle C\cdot{x^2}+k$ is the anti-derivative of $\displaystyle C\cdot{2}\cdot{x}$

That's denoted as follows: $\displaystyle \int{C\cdot{2}\cdot{x}}\cdot{dx}=C\cdot{x^2}+k$

To find the constant k you use the other information you have

4. Oh sorry, I didn't realised it was $\displaystyle f(x)=4\cdot{e^{2x}}$ that you wanted.
Well, for this case given $\displaystyle y=C\cdot{e^{2x}}+k$ derivating we have: $\displaystyle y'=2\cdot{C}\cdot{e^{2x}}$ where C and k are real numbers