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.

1 answer:

5 0

$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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$\text{Hey there!}$

$\mathsf{\dfrac{2}{3}x+2-x-3}\\\\\mathsf{COMBINE\ your\ like\ terms}\\\\\mathsf{(\dfrac{2}{3}x-x)+(2-3)}\\\\\mathsf{\dfrac{2}{3}x-x=\dfrac{-1}{3}}\\\\\mathsf{2-3=-1}\\\\\boxed{\boxed{Thus,\ your \ answer\ is: \boxed{\dfrac{-1}{3}x -1}}}\checkmark$

$\text{Good luck on your assignment and enjoy your day!}$

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