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JAMB Mathematics 2018 Paper

Question : 37

Total: 62

^2

- 2x

Solution:

Concept:

The slope of the tangent to a curve at a given point is the value of the derivative

\frac{dy}{dx}

at that point.

Explanation:

Differentiate the curve

y = x^2 - 2x

with respect to

x

\frac{dy}{dx} = 2x - 2

At the point

(2, 0)

, substitute

x = 2

\frac{dy}{dx} = 2(2) - 2 = 4 - 2 = 2

So the gradient of the tangent is

m = 2

Use the point-slope form of a line through

(x_1, y_1) = (2, 0)

y - y_1 = m(x - x_1)

y - 0 = 2(x - 2)

y = 2x - 4

Answer:

The equation of the tangent is

y = 2x - 4

, which is option A.

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