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.
from dy/dx = 4x + 7x
y = 2x^2 + 7x + c
but 4x+7 = 5
4x = -2
x = -1/2
sub into y = 2x
y = 2(-1/2) = -1
so P is (-1/2, -1)