Question

if f(2)=3 and f'(2)=5 find and equation of the tangent line and the normal line to the graph of y=f(x)

Answer 1

you have the point and the slope, so use the point - slope formula
\[y-y_1=m(x-x_1)\] with
\[m=5, x_1=2,y_1=3\]

Answer 2

how do you know that the slope is 5?

Answer 3

because the derivative is the slope of the tangent like. or rather the derivative gives the slope of the tangent line

Answer 4

you are told
\[f'(2)=5\] which means at
\[(2,3)\] the slope of the tangent line is 5

Answer 5

okay thanks a lot what is the difference between f(x) and f'(x)?

Answer 6

. . . f'(x) is the derivative of f(x) . . .

By asking that you basically just told Satellite that you weren't listening to a word he was saying when he was wasting his time trying to explain the problem to you. -_-'