Find the function with derivative f′(x)=e^(5x) that passes through the point P=(0,6/5).

Question

f(x)=

Answer 1

f′(x)=e^(5x)
f(x) = (1/5) e^(5x) + c
given f(0) = 6/5

0 = (1/5) e^0 + c
c = -1/5

f(x) = (1/5) e^(5x) - 1/5