Question

The equation of a curve is y=f(x). the curve goes through the points (1,3) and (3,7). f'(x) = 4x+p, where p is a number.

Answer 1

$f'(x)=4x+p\\ f(x)=2x^2+px+C\\\\ 3=2\cdot1^2+p\cdot1+C\\ 7=2\cdot3^2+p\cdot3+C\\\\ 3=2+p+C\\ 7=18+3p+C\\\\ C=1-p\\ 3p=-11-C\\\\ 3p=-11-(1-p)\\ 3p=-11-1+p\\ 2p=-12\\ p=-6\\\\ C=1-(-6)\\ C=7\\\\ y=2x^2-6x+7$