Question

How to find the function with derivative f′(x)=e^(7x) that passes through the point P=(0,8/7) ?

Answer 1

f(x)= `1/7 e^(7x)` +1

Explanation:

Given, f'(x) = `e^(7x)`

Hence f(x)= `1/7 e^(7x)` +C. This function passes through (0,8/7), therefore `8/7= 1/7` +C

C=1, f(x)= `1/7 e^(7x)` +1