Differentiation

WMA12Topic 2.72 questions

Increasing and decreasing functions, stationary points and optimisation.

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Original practice questions written in the style of the exam.

2

500

A1

A = x^2 + 4xh = x^2 + \dfrac{2000}{x}

shown (1)

M1 Differentiates: at least one term correct (1)

A1

\dfrac{dA}{dx} = 2x - \dfrac{2000}{x^2}

(1)

M1 Sets

\dfrac{dA}{dx} = 0

and solves:

x^3 = 1000

,

x = 10

(1)

A1 Minimum

A = 300\,\text{cm}^2

(1)

B1

\dfrac{d^2A}{dx^2} = 2 + \dfrac{4000}{x^3} = 6 > 0

, so minimum (1)