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
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #8694)