Question

Find the equation of the tangent line for the function f(x)=x+sqrt(c). at x=1 ?

Answer 1

Whenever you see "equation for the tangent line for..."

just think... I need to know the slope of that line and either an intercept or a point on that line. Algebra tells you that given a slope and a point or an intercept (also a point), you can write a line equation

Answer 2

So, what is the slope of f(x)?

It is the first derivative of f(x). So, the tangent line to f(x) at ANY point along f(x) has a slope that is equal to the slope of f(x) at that point.

Of course, the slope of f(x) depends on where you are... what x value you are at... along f(x). Luckily they tell you... :) it's at x=1