Find the point (x, y) on the Euclidean plane where the curve y = 2×2…

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

Correct Answer: Option A

Explanation

Equation of curve;
y = 2x² – 2x + 3
gradient of curve;
(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)