1 of 8 0-day streak

Locate a polynomial turning point numerically

Question 1 of 8

Calculator allowed

Use the supplied polynomial and a sequence of value tables to obtain an approximate coordinate pair

P(x)=-\frac{1}{2}x^{3} - \frac{15}{4}x^{2} - 6x + \frac{119}{12}

The model output is \(P(x)\) for inputs in the meaningful domain \(x\in[-3, 2]\)

Graph of the polynomial over the stated model domain

The model domain supplies the initial window. Complete the table in order and give both coordinates to 1 decimal place

(a)1 mark

Which interval and extremum type are consistent with the polynomial and the first table?

Use \(x\in[-3, 2]\). The stationary point is \(a local minimum\)

Use \(x\in[-2, 3]\). The stationary point is \(a local minimum\)

Use \(x\in[-3, 2]\). The stationary point is \(a local maximum\)

Use \(x\in[-4, 1]\). The stationary point is \(a local maximum\)

(b)3 marks

Complete the coarse table. The input step is \(\frac{1}{4}\); leave the supplied entries unchanged and enter the missing exact values

\(P(-\frac{23}{16})\) \(P(-\frac{19}{16})\) \(P(-\frac{11}{16})\)

Give the approximate horizontal coordinate of the maximum to 1 decimal place

horizontal coordinate \(x\)

Format: 1 d.p.

(d)1 mark

Give the corresponding approximate output value to 1 decimal place

corresponding output \(P(x)\)

Format: 1 d.p.

(e)1 mark

Which interpretation is supported by the refined table and the stated domain?

The model output has a local maximum near x=12.7; the model output there is about -0.9 units

The first table gives its maximum at x=-0.9; its model output is about 13.7 units

The model output has a local minimum near x=-0.9; the model output there is about 12.7 units

The model output has a local maximum near x=-0.9; the model output there is about 12.7 units