Given that the graph of f(x) passes through the point (2,5) and that the slope of its tangent line at (x, f(x))is 3x+5, what is f(3) ?

Answer 1

if dy/dx = 3x+5 , then
y = (3/2)x^2 + 5x + c

when x=2, y = 5
5 = (3/2)(4) + 10 + c
5 = 6 + 10 + c
c = -11

f(x) = (3/2)x^2 + 5x - 11
f(3) = (3/2)(9) +15 - 11 = 35/2