Final answer:
To find the function with derivative f'(x) = e^5 that passes through the point P(0, 6/5), integrate the derivative to find the original function and solve for the constant of integration using the given point.
Step-by-step explanation:
To find the function with derivative f'(x) = e^5 that passes through the point P(0, 6/5), we can start by integrating the derivative to find the original function. The integral of e^5 with respect to x is e^5x + C, where C is the constant of integration. Now we can use the given point to solve for the constant C.
Plugging in x = 0 and y = 6/5 into the original function, we get:
e^5(0) + C = 6/5
Simplifying further:
C = 6/5
So the function that satisfies the given conditions is:
f(x) = e^5x + 6/5