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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

Options

A) (1, 3)

B) (2, 7)

C) (0, 3)

D) (3, 15)

The correct answer is 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)

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Dicussion (1)

  • 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)

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