Find the function f(x) described by the given initial value problem
f'(x)=6^x, f(1)=0
6 answers
To find f(x), first you need to integrate f'(x).
f(x)6^x ln(6)
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) = ....
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) = ....
Hmmm. seems to me that
∫ a^x dx = 1/lna * a^x + C
∫ a^x dx = 1/lna * a^x + C
good catch
I multiplied instead of divided.
I multiplied instead of divided.
∫ 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
0=6^x dx= 1ln(6) * 6^x + C
is this right so far
3 answers