TMUA Practice Question — Worked Solution

P1·Differentiation, Integration·7.0Mock 0 · P1 · Q19

area between curvestranslationcubicoptimisationstationary pointdefinite integral

The curve

C

has equation

y = x^{3} - 3 x + 2

The curve

C^{'}

is obtained by translating

C

k

units in the positive

x

-direction, where

k > 0

.For some values of

k

, the curves

C

and

C^{'}

enclose a finite region. What is the greatest possible area of this region, as

k

varies?

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