Week 9 - Graded Assignment 9

Course: Jan 2026 - Mathematics I

Week 9 - Graded Assignment 9

Last Submitted: You have last submitted on: 2026-04-17, 05:42 IST

Introduction

Suppose $f_1(x)= x^3$ and $f_2(x)=x$ denote the profits of Company A and Company B, respectively, throughout 1 year (the beginning of the year is denoted by $x=0$ and the ending denoted by $x=1$). The predicted profits of Company A and Company B in the same year are given by the functions $g_1(x)=\sqrt{x}$ and $g_2(x)=e^x$, respectively. The curves represented by the functions $f_1$ and $g_1$ are shown in Figure M2W3G2, and the curves represented by the functions $f_2$ and $g_2$ are shown in Figure M2W3G3.

Question 1

• i) $\rightarrow$ b) $\rightarrow$ 1), iii) $\rightarrow$ a) $\rightarrow$ 2).
• i) $\rightarrow$ b) $\rightarrow$ 3), ii) $\rightarrow$ c) $\rightarrow$ 1).
• ii) $\rightarrow$ c) $\rightarrow$ 1), iii) $\rightarrow$ a) $\rightarrow$ 2).
• i) $\rightarrow$ b) $\rightarrow$ 1), ii) $\rightarrow$ c) $\rightarrow$ 3), iii) $\rightarrow$ a) $\rightarrow$ 2).

Question 2

                                      

• The cylinder has maximum volume amongst all cylinders which can be inscribed when $h= R$.
• The cylinder has maximum volume amongst all cylinders which can be inscribed when $h= \sqrt{3}R$.
• The cylinder has maximum volume amongst all cylinders which can be inscribed when $h= \frac{R}{\sqrt{3}}$.
• The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when $h=2R$.
• The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when $h=\frac{R}{\sqrt{2}}$.
• The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when $h=\sqrt{2}$.

Question 3

• Curve 1
• Curve 2
• Curve 3
• Curve 4

Question 4

Question 5

• The error in prediction for company A is $\frac{5}{12}$.
• The error in prediction for company A is $\frac{11}{12}$.
• The error in prediction for company A is more than that for company B.
• The error in prediction for company B is more than that for company A.
• The error in prediction for Company A and Company B, cannot be compared using the given information.

Question 6

Question 7

Question 8

Question 9