Find values of A for two functions tangent at a point

[Painguy]

Homework Statement

For what values of a are y=a^x and y=1+x tangent at x=0? Explain

Homework Equations

y1=1+x
y2=a^x
y2'=a^xln(a)
y1'=1

The Attempt at a Solution

Since both equations are tangent at x=0 i set their derivatives equal to each other in hopes of getting a a^xln(a)=1 I then substitute x in that equation with 0 and end up with ln(a)=1.
I end up with a = e. Is this correct?

 

[Dick]

Homework Statement

For what values of a are y=a^x and y=1+x tangent at x=0? Explain

Homework Equations

y1=1+x
y2=a^x
y2'=a^xln(a)
y1'=1

The Attempt at a Solution

Since both equations are tangent at x=0 i set their derivatives equal to each other in hopes of getting a a^xln(a)=1 I then substitute x in that equation with 0 and end up with ln(a)=1.
I end up with a = e. Is this correct?

It sure is correct. You also checked that y1(0)=y2(0), yes?

 

[Painguy]

It sure is correct. You also checked that y1(0)=y2(0), yes?

No i did not, but in hindsight i should have done that. Thanks for the reminder :)