Analyse polynomial curves, stationary points and extrema practice questions | Mathematical Methods (Year 11, VCE Units 1 & 2, Differentiation and applications, Curve analysis and stationary points)

(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,-2],\quad D=[-2,\infty)

I=(-2,\infty),\quad D=(-\infty,-2)

I=(-\infty,-2),\quad D=(-2,\infty)

(d)1 mark

Classify the stationary point from the derivative sign change

It is not stationary

A stationary point of inflection

A local minimum

A local maximum