Asked by Natasha Roberts

Find the function f(x) described by the given initial value problem
f'(x)=6^x, f(1)=0
Answered by Leo
To find f(x), first you need to integrate f'(x).
Answered by Natasha Roberts
f(x)6^x ln(6)
Answered by Reiny
good start

f(x) = ln6*6^x + c
given : f(1) = 0 ----> implies that (1,0) satisfies the equation

0 = ln6(6^0) + c , but 6^0 = 1
c = -ln6

then f(x) = ....
Answered by oobleck
Hmmm. seems to me that
∫ a^x dx = 1/lna * a^x + C
Answered by Reiny
good catch
I multiplied instead of divided.
Answered by Natasha Roberts
∫ 6^x dx = 1/ln(6) * 6^x + C ,f(1)=0
0=6^x dx= 1ln(6) * 6^x + C
is this right so far
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