Why isn't the answer to TMUA-P1-MM6-008 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM6-008 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM6-008?

No — calculators are banned in the TMUA. TMUA-P1-MM6-008 is set for a no-calculator target of about 210 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM6-008?

TMUA-P1-MM6-008 is Paper P1 · Differentiation (specification code MM6), level 2. Drill more of the same topic from this page.

TMUA-P1-MM6-008 — Paper P1 · Differentiation · Level 2

P1MM6Level 2~210s target

Spec: MM6 · No calculator · ~210s

The curve

y = x^3 - 3x

has a local maximum. What is its

y

-value?

Options

$-2$
$1$
$-1$
$2$
$0$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: stationary-points, max-min-swap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

\frac{dy}{dx} = 3x^2 - 3 = 0

gives

x = \pm 1

; the second derivative

6x

is negative at

x = -1

, so the maximum value is

(-1)^3 - 3(-1) = 2

. Trap:

-2

is the minimum value (at

x = 1

) — plausible if you find both stationary values but swap them.

Keep practising

Same topic · same level
P1MM6Level 2
TMUA-P1-MM6-004
Differentiate y = √x^3 (for x > 0 ) with respect to x.
Differentiation
Open TMUA-P1-MM6-004 →
Same trap: max-min-swap
P1MM4Level 2
TMUA-P1-MM4-010
What is the maximum value of y = 3 - 2 x?
Trigonometry
Open TMUA-P1-MM4-010 →
Step up a level
P1MM6Level 3
TMUA-P1-MM6-009
The area of a circle is A = π r^2. The radius increases at 2 cm/s. At what rate is the area increasing when r = 5 cm?
Differentiation
Open TMUA-P1-MM6-009 →

Browse more

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Keep practising

Same topic · same level

P1MM6Level 2

TMUA-P1-MM6-004

Differentiate y = √x^3 (for x > 0 ) with respect to x.

Differentiation

Open TMUA-P1-MM6-004 →

Same trap: max-min-swap

P1MM4Level 2

TMUA-P1-MM4-010

What is the maximum value of y = 3 - 2 x?

Trigonometry

Open TMUA-P1-MM4-010 →

Step up a level

P1MM6Level 3

TMUA-P1-MM6-009

The area of a circle is A = π r^2. The radius increases at 2 cm/s. At what rate is the area increasing when r = 5 cm?

Differentiation

Open TMUA-P1-MM6-009 →

TMUA-P1-MM6-008 — Paper P1 · Differentiation · Level 2

Options

Keep practising

Master Differentiation

TMUA-P1-MM6-008 — Paper P1 · Differentiation · Level 2

Options

Keep practising

Master Differentiation