Analyse polynomial curves, stationary points and extrema practice questions | Mathematical Methods (Year 12, VCE Units 3 & 4, Applications of differentiation, Tangents, normals and curve sketching)

(a)2 marks

Enter every coefficient in descending powers, including zero for an absent term

f'(x)=A_1x+A_0

\(\text{coefficient of }x\) \(\text{constant coefficient}\)

(b)2 marks

Enter every stationary input and its original-function height, in increasing input order

\(x_1\) \(f(x_1)\)

(c)1 mark

Select the increasing (I) and decreasing (D) derivative-sign intervals. Report derivative-sign intervals as open intervals split at every derivative zero, even when the sign does not change. Do not include stationary inputs in those reported intervals

I=\mathbb R,\quad D=\varnothing

I=(-\infty,\frac{1}{2}),\quad D=(\frac{1}{2},\infty)

I=(-\infty,\frac{1}{2}],\quad D=[\frac{1}{2},\infty)

I=(\frac{1}{2},\infty),\quad D=(-\infty,\frac{1}{2})

(d)1 mark

Classify the stationary point from the derivative sign change

It is not stationary

A local maximum

A stationary point of inflection

A local minimum