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# Find the point (x, y) on the Euclidean plane where the curve y = 2x2 - 2x + 3 ha...

### Question

Find the point (x, y) on the Euclidean plane where the curve y = 2x2 - 2x + 3 has 2 as gradient

A) (1, 3)

B) (2, 7)

C) (0, 3)

D) (3, 15)

### Explanation:

Equation of curve;
y = 2x2 - 2x + 3
$$\frac{dy}{dx}$$ = differential coefficient
$$\frac{dy}{dx}$$ = 4x - 2, for gradient to be 2
∴ $$\frac{dy}{dx}$$ = 2
4x - 2 = 2
4x = 4
∴ x = 1
When x = 1, y = 2(1)2 - 2(1) + 3
= 2 - 2 + 3
= 5 - 2
= 3
coordinate of the point where the curve; y = 2x2 - 2x + 3 has gradient equal to 2 is (1, 3)

## Dicussion (1)

• Equation of curve;
y = 2x2 - 2x + 3
$$\frac{dy}{dx}$$ = differential coefficient
$$\frac{dy}{dx}$$ = 4x - 2, for gradient to be 2
∴ $$\frac{dy}{dx}$$ = 2