JAMB 2000 · UME · Q39

Calculus (JAMB bridge)

A function $f(x)$ passes through the origin and its first derivative is $3x + 2$ . What is $f(x)$ ?

Worked solution (try it first)

Integrate the derivative: $f(x) = \frac32x^2 + 2x + c$ .
The curve passes through the origin, so $f(0) = 0$ and $c = 0$ .
So $y = \frac32x^2 + 2x$ , option A.

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