Sep 17, 2012 Thread starter #1 B 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 $a$

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 $a$

Sep 17, 2012 #2 P Plato Well-known member MHB Math Helper Jan 27, 2012 196 Bushy said: 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 $a$ Click to expand... 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 said: 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 $a$ Click to expand... The equation of the tangent line is $y-f(a)=f^{\prime}(a)(x-a)$. Now let $x=0~\&~y=0$ then solve for $k$.

Sep 18, 2012 Thread starter #3 B Bushy Member Jul 2, 2012 40 $y-f(a) = f'(a)(x-a)$ and $0-(e^a+k) = e^a(0-a)$ so $k=e^a(a-2)$