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Tangent to a curve

Bushy

Member
Jul 2, 2012
40
Hi there,

The function $f(x)= e^x+k$ has a tangent to the curve at $x=a$ and going through the origin. Find $k$ in terms of $a$
 

Plato

Well-known member
MHB Math Helper
Jan 27, 2012
196
The function $f(x)= e^x+k$ has a tangent to the curve at $x=a$ and going through the origin. Find $k$ in terms of $a$
The equation of the tangent line is $y-f(a)=f^{\prime}(a)(x-a)$.
Now let $x=0~\&~y=0$ then solve for $k$.
 

Bushy

Member
Jul 2, 2012
40
$y-f(a) = f'(a)(x-a)$

and

$0-(e^a+k) = e^a(0-a)$

so

$k=e^a(a-2)$