Mathematics

The gradient of a curve is 2x + 7 and the curve passes through point…

The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). find the equation of the curve.
  • A.
    y = x2 + 7x + 9
  • B.
    y = x2 + 7x – 18
  • C.
    y = x2 + 7x + 18
  • D.
    y = x2 + 14x + 11
Correct Answer: Option B
Explanation

dy/dx = 2x + 7
y = ∫2x + 7
y = x2 + 7x + C at (2,0)
0 = 22 + 7(2) + C
0 = 4 + 14 + C
0 = 18 + C
C = -18
∴ The equation is y = x2 + 7x – 18