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(c) cut from each corner of length x cm, a maximum volume for the resulting open-top cake tin will be obtained. Show sufficient working to support your conjecture. Present a conjecture based on a square piece of tinplate of side length I cm, which when a square is

(c) cut from each corner of length x cm, a maximum volume for the resulting open-top cake tin will be obtained. Show sufficient working to support your conjecture. Present a conjecture based on a square piece of tinplate of side length I cm, which when a square is

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Present a conjecture based on a square piece of tinplate of side length x cm, which when a square is cut from each corner of length x cm, a maximum volume for the resulting open-top cake tin will be obtained. Show sufficient working to support your conjecture.

Let I (cm) be the side length of the square tinplate and let x (cm) be the side length of the square cuts to be made. (a) Given l = 10cm, show that the volume of the cake tin can be expressed as V(x) = 4x3 – 40x² + 100x cm³. Hence, determine V'(x) and find the exact value of x which will maximise the volume of the cake tin. - (b) Further this investigation by determining the exact value of x for at least two other values of I cm (side length of square tinplate). (c) Present a conjecture based on a square piece of tinplate of side length I cm, which when a square is cut from each corner of length x cm, a maximum volume for the resulting open-top cake tin will be obtained. Show sufficient working to support your conjecture.
Transcribed Image Text:Let I (cm) be the side length of the square tinplate and let x (cm) be the side length of the square cuts to be made. (a) Given l = 10cm, show that the volume of the cake tin can be expressed as V(x) = 4x3 – 40x² + 100x cm³. Hence, determine V'(x) and find the exact value of x which will maximise the volume of the cake tin. - (b) Further this investigation by determining the exact value of x for at least two other values of I cm (side length of square tinplate). (c) Present a conjecture based on a square piece of tinplate of side length I cm, which when a square is cut from each corner of length x cm, a maximum volume for the resulting open-top cake tin will be obtained. Show sufficient working to support your conjecture.
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