a curve is such that dy/dx=4x+7. the line y=2x meets the curve at point 'P'. Given that the gradient of the curve at P is 5. State the coordinates of P.

Answer 1

y=2x^2+7x+c
5=4x+7, so x = -1/2
y(-1/2) = -3+c

at x = -1/2, y=2x = -1, so

-1 = -3+c
c=2

y = 2x^2+7x+2

P=(-1/2,-1)