# Math Help - 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 $f'(x) = 4e^(2x)$ and $f(0) = 1$, find the function $f(x)$?

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

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

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

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 $f(x)=C\cdot{x^2}+k$ where C and k are real numbers, derivating: $f'(x)=C\cdot{2}\cdot{x}$

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

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

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

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

this seems to work but i don't think we've gone over anti-derivatives yet. so far this section we've only gone over implicit differentiation, related rates, increments, linear approximation, increasing and dec functions, mean value theorem, and the first derivative test.

4. Oh sorry, I didn't realised it was $f(x)=4\cdot{e^{2x}}$ that you wanted.
Be careful when writing the exponent f(x)=4\cdot{e^{2x}}

Well, for this case given $y=C\cdot{e^{2x}}+k$ derivating we have: $y'=2\cdot{C}\cdot{e^{2x}}$ where C and k are real numbers