What is being asked for in the question "What is an equation of the line tangent to f(x) at its y-intercept?

Question

All i wish to know is what is being asked for when asked to find an equation of a tangent line at its y intercept. Are they asking for equation of the tangent line in terms of y intercept form?

Answer 1

If your function is $y=f(x)$ then they are asking for the equation of the tangent line at the point $(0,f(0))$.

So you have to find the slope $m$ at that point using $m=f^\prime(0)$ and you already have the point $(0,f(0))$, so you use the point-slope equation of a line.

Answer 2

Using calculus find the slope of the line at $(0,g(0))$ . Let it be $m$. Then you can find equation of tangent as $y-y1=m(x-x1)$ where $y1=g(0) , x1=0$. NOTE: $g(x)$ is a function of $x$ and $m$=$g'(0)$ i.e. you need to differentiate your function w.r.t $x$ and put that value of $x$ where you want the slope of tangent.