Question 38

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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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