What is the x-coordinate of the stationary point of the curve y = 3x^2 - 12x + 7? — JAMB UTME

What is the $x$ -coordinate of the stationary point of the curve $y = 3x^2 - 12x + 7$ ?

The

x

-coordinate of the stationary point is

2

To find the stationary point, take the derivative of

y = 3x^2 - 12x + 7

with respect to

x

, obtaining

\frac{dy}{dx} = 6x - 12

. Setting the derivative equal to zero gives

6x - 12 = 0

, which solves to

x = 2

Differentiate the equation of the curve with respect to

x

\frac{dy}{dx} = 6x - 12

Stationary points occur where the first derivative (gradient) of the function is equal to zero.

Set the derivative to zero and solve for

x

6x - 12 = 0 \implies 6x = 12 \implies x = 2

Solving this linear equation gives the exact value of

x

at which the tangent to the curve is horizontal.

Stationary Points of a Curve

Estimated Time:45s

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