Suppose that f(x) is a differentiable function. If lim x->2 (f(x)-3)/(x-2) = 4...

Question

Suppose that f(x) is a differentiable function. If lim x->2 (f(x)-3)/(x-2) = 4, find:

F(2)

f'(2)

The equation of the line through (2, f(2) ) tangent to the graph y = f(x)

Answer 1

The given limit is of the form that is the limit definition of the derivative at a point: f ‘ (a) = lim_x→a(f(x)-f(a))/(x—a)

So, f(2) = 3 , f ‘ (2) = 4 and use the point (2,3) and the slope = 4 to write the tangent line equation in point-slope form.