Question

Find the function with the given derivative whose graph passes through the point P.

Answer 1

fprime(x)=e^(2x) P(0,3/2)

Answer 2

so you have to integrate or find the anti-derivative of f ' (x)=e^(2x).

Then use the point to determine the value of c.

Answer 3

how would you go about finding the anti derivative of an exponential?

Answer 4

\[\frac{ d }{ dx }e^x=e^x\]

Answer 5

\[\frac{ d }{ dx}e^{f \left( x \right)}=f^{\prime}\left( x \right)\cdot e^{f \left( x \right)}\]

Answer 6

f(0)=2e^(2x)?

Answer 7

\[\int\limits f^{\prime}\left( x \right)\cdot e^{f \left( x \right)}\,\,dx=e^{f \left( x \right)}+C\]

Answer 8

no, find f(x) first. to be sure you have the correct function, take its derivative and verify that it equals the derivative function you were given.

Answer 9

once you have the correct function, then evaulate it when x = 0 and set the result equal to 3/2. remember, you will have a constant of integration. the derivative of a constant is 0 and that is why it doesn't show in the derivative.

Answer 10

you there?