Question

Let f(x)=b^x be an exponential function such that
f '(0)=1 Find b

Answer 1

by f' you mean the derivative yes?

Answer 2

yes, thanks

Answer 3

Well, what is the derivative of b^x ?

Answer 4

The value of b is e.

Answer 5

how did you get there?

Answer 6

It is a mathematical constant equal to 2.718(approx.) You must be knowing, I guess.

Answer 7

I know what e is, how did you solve

Answer 8

Did you take the derivative of f ?

Answer 9

\[f'(x)=b^x\ln(b)\]

Answer 10

Take log on both sides and then differentiate.

Answer 11

You'll get the equation posted by Zarkon. Solve it by subs. x=0.

Answer 12

If you had found the derivative (as Zarkon has given) you could plug in for
\[1 = b^0(ln\ b)\]

And find that ln(b) = 1 Therefore b = e.

Answer 13

Did you get it? Or do you want a detailed working of the problem?

Answer 14

got it thanks

Answer 15

Next time, don't be afraid to differentiate =)

Answer 16

It's often not as bad as it seems.