JAMB 1994 · UME · Q40

Calculus (JAMB bridge)

Find the point $(x, y)$ where the curve $y = 2x^2 - 2x + 3$ has gradient 2.

Worked solution (try it first)

The gradient is $\frac{dy}{dx} = 4x - 2$ .
Set it equal to 2: $4x - 2 = 2$ , so $4x = 4$ and $x = 1$ .
Then $y = 2 - 2 + 3 = 3$ , so the point is $(1, 3)$ , option A.

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