Given that the graph of f(x) passes through the point (8,6) and that the slope of its tangent line at (x,f(x)) is 5x+4, what is f(3)?

Answer 1

f'(x) = 5x + 4

Integrate to get f(x) = (5/2)x² + 4x + C

Since (8,6) is on the graph of y = f(x), f(8) = 6.

So, 160 + 32 + C = 6. Therefore, C = 6 - 192 = -186

f(3) = 45/2 + 12 - 186 = -151.5