Question

Find the function f(x) described by the given initial value problem.
f′(x)=6x,f(1)=0

6^x dx = 1/ln(6) * 6^x + C

Answer 1

f'(x) = 6^x
so, you have f(x) = 1/ln6 * 6^x + c
f(1) = 0, so
1/ln6 * 6 + c = 0
c = -6/ln6
so, f(x) = 1/ln6 * 6^x - 6/ln6

Answer 2

Find the function f(x) described by the given initial value problem.
f′(x)=8^x , f(2)=1

f'(x) = 8^x
so, you have f(x) = 1/ln8 * 8^x + c
f(2) = 1, so

1/ln8 * 8 + c = 0

Answer 3

do you then take the f(2)=1 and make it
=1/ln8*8^x+c
f(2)=1/ln8*8^x+c=1
c=-1/ln8*-8^+1
c=-9/ln8