Calculus tangent lines

Question

Find the c intercept of the tangent line at the point P (3,3) on the graph of f when

lim ( f(3 + h) - 3 ) / h = 3

h-> 0

Answer 1

so the derivative at 3 is 3

f ' (3) = 3

the slope of the tangent line is 3.

the tangent line must eat (3,3).

c = y - mx = 3 - 3(3) = 3 - 9 = -6

the tangent line has equation y = 3x-6

so the intercept is c=-6