Jambmaths question:
The function f (x) passes through the origin and its first derivative is 3x + 2. What is f(x)?
Option A:
$y=\tfrac{3}{2}{{x}^{2}}+2x$
Option B:
$y=\tfrac{3}{2}{{x}^{2}}+x$
Option C:
$y=3{{x}^{2}}+\tfrac{x}{2}\text{ }$
Option D:
$y=3{{x}^{2}}+2x$
Jamb Maths Solution:
$\begin{align} & {{f}^{1}}(x)=3x+2 \\ & f(x)=\int{(3x+2)dx}=\tfrac{3{{x}^{2}}}{2}+2x+c \\ & \text{Since }f(x)\text{ pass through the origin, when }x\text{ }=0,f(x)=0 \\ & 0=\tfrac{3{{(0)}^{2}}}{2}+2(0)+c;\text{ }c=0 \\ & f(x)=\tfrac{3{{x}^{2}}}{2}+2x \\\end{align}$
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