Dark mode

Further applications of differentiation — Question 212

Original QCE Vault practice · 5 marks

Q212 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 212 (5 marks)

Let

f(x)=x^{3}-6x^{2}+9x+4

.

a)

Find all stationary

x

-values.

[2 marks]

b)

Classify the stationary points.

[2 marks]

c)

Find the coordinates of the local maximum.

[1 mark]

Question linkSyllabus coverage

Related questions

Q3 · Original practice · 1 mark
The graph shown is the graph of $f'(x)$ . At which value of $x$ does $f$ have a local maximum?
Further applications of differentiation
Q13 · Original practice · 1 mark
The stationary points of $f(x)=x^3-3x^2-9x+4$ occur when $x=$
Further applications of differentiation
Q23 · Original practice · 1 mark
For $f(x)=xe^{-x}$ on $x>0$ , the $x$ -coordinate of the maximum point is
Further applications of differentiation
Q28 · Original practice · 4 marks
A rectangle is inscribed symmetrically under the parabola $y=12-x^2$ and above the $x$ -axis, as shown. The upper right corner is $(x,12-x^2)$ , where $0<x<\sqrt{12}$ . Determine the maximum possible area of the rectangle.
Further applications of differentiation