1 of 8 0-day streak

Solve a maximum or minimum problem by differentiation

Question 1 of 8

No calculator

The perimeter of a rectangle is fixed at \(48\,\mathrm{cm}\). Determine the area that is maximised

Let \(w\) be the first length and \(l\) the second length

2w+2l=48

A(w,l)=wl

The practical domain is \(w\in\left[0,24\right]\)

Determine the requested maximum or minimum from the one-variable model

(a)1 mark

Select the correct one-variable objective after using the displayed data

A(w,l)=wl

A(w)=-w^{2} + 24\,w

A(w)=48\div 2-w

(b)4 marks

Complete the numerical table for the constraint and the one-variable objective

Given constant in the constraint coefficient of w to the power 2 coefficient of w constant term

Select the practical domain for \(w\)

w\in\left[0,24\right]

w\in\mathbb{R}

w\in\left[0,48\right]

(d)6 marks

Complete the candidate table. Enter every stationary input and the objective value at each listed input

Left endpoint input Objective at the left endpoint Stationary input 1 Objective at stationary input 1 Right endpoint input Objective at the right endpoint

(e)1 mark

Find the input value \(w\) that gives the stated maximum

Optimal value of w (centimetres)

Format: Exact value

(f)1 mark

Find the maximum objective value

maximum objective value (square centimetres)

Format: Exact value