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millsey18 millsey18
  • 05-11-2014
  • Mathematics
Answered

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.

Afind the value of p
Bfind the equation of the curve

Please help asap!

Verified Answer :

konrad509
konrad509 konrad509
  • 05-11-2014

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

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