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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.
a) find the value of p
b) find the equation of the curve
Please help asap!



Answer :

konrad509
[tex]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 [/tex]

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