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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

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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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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