Find values of A for two functions tangent at a point

  • Thread starter Painguy
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  • #1
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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?
 

Answers and Replies

  • #2
Dick
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Homework Helper
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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?
 
  • #3
120
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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 :)
 
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