JAMB 1998 · UME · Q41

Calculus (JAMB bridge)

Find the equation of the curve which passes through the point $(2, 5)$ and whose gradient at any point is $6x - 5$ .

Worked solution (try it first)

Integrate the gradient: $y = 3x^2 - 5x + c$ .
The curve passes through $(2, 5)$ : $5 = 12 - 10 + c$ , so $c = 3$ .
So $y = 3x^2 - 5x + 3$ , option D.

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