Given that the graph of f(x) passes through the point (3,4) and that the slope of its tangent line at (x,f(x)) is 4x+3, what is f(5) ?

Answer 1

The slope of the tangent line at (x,f(x)) is f^'(x), so

f^'(x)=4x+3, then f(x)=2x^2+3x+c, we also know that f(3)=4, since (3,4) is a point on f(x).

f(3)=2*3^2+3*3+c=4

2*9+9+c+4

18+9+c=4

27+c=4

c=-23

and f(x)=2x^2+3x-23

then

f(5)=2*5^2+3*5-23=2*25+15-23=50+15-23=42