MHB Tangent to Curve $e^x+k$ at $x=a$: Find $k$

[Bushy]

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 $a$

 

[Plato2]

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]

$y-f(a) = f'(a)(x-a)$

and

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

so

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