Jambmaths question:
The gradient of a curve is 2x + 7 and the curve passes through point (2,0). Find the equation of the curve
Option A:
$y={{x}^{2}}+4x+11$
Option B:
$y={{x}^{2}}+7x+9$
Option C:
$y={{x}^{2}}+7x-18$
Option D:
$y={{x}^{2}}+7x+18$
Jamb Maths Solution:
$\begin{align} & \text{Each time we differentiate a function, we actually finding its gradient or slope} \\ & m=\frac{dy}{dx} \\ & \frac{dy}{dx}=2x+7 \\ & y=\int{(2x+7)dx} \\ & y={{x}^{2}}+7x+c \\ & \text{At point }(2,0) \\ & 0={{2}^{2}}+7(2)+c \\ & c=-18 \\ & \text{The particular solution is }y={{x}^{2}}+7x-18 \\\end{align}$
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