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2. The function below, and its graph, gives the rainfall in mm/day that falls in the month of May, where t is measured in days and t = 0 coincides with 1 May 2022. 50 f(t) = t2 - 20t + 101 (a) Showing all your calculations find the following: i. The day on which the rainfall was highest. ii. The day on which the rainfall per day was increasing the fastest. (b) What does the integral S”. f(t)dt calculate? Explain clearly, but you do not need to actually calculate the integral. (c) If F(t) is an antiderivative of f(t), explain why the function F(t) is always increasing. (d) You are told that a total of 150mm of rain fell in May 2022. Using this fact draw a rough sketch of the antiderivative function F(t) of f(t) starting with F(0) = 0. Indicate any important aspects of the graph - maxima, minima, inflection points etc. (You do not need to find the formula for F(t) just make a rough sketch using what you know about f(t).)

2. The function below, and its graph, gives the rainfall in mm/day that falls in the month of May, where t is measured in days and t = 0 coincides with 1 May 2022. 50 f(t) = t2 - 20t + 101 (a) Showing all your calculations find the following: i. The day on which the rainfall was highest. ii. The day on which the rainfall per day was increasing the fastest. (b) What does the integral S”. f(t)dt calculate? Explain clearly, but you do not need to actually calculate the integral. (c) If F(t) is an antiderivative of f(t), explain why the function F(t) is always increasing. (d) You are told that a total of 150mm of rain fell in May 2022. Using this fact draw a rough sketch of the antiderivative function F(t) of f(t) starting with F(0) = 0. Indicate any important aspects of the graph - maxima, minima, inflection points etc. (You do not need to find the formula for F(t) just make a rough sketch using what you know about f(t).)

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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2. The function below, and its graph, gives the rainfall in mm/day that falls in the month of May, where t is measured in days and t = 0 coincides with 1 May 2022. f(t) = 50 t²20t + 101 (a) Showing all your calculations find the following: i. The day on which the rainfall was highest. ii. The day on which the rainfall per day was increasing the fastest. (b) What does the integral f(t)dt calculate? Explain clearly, but you do not need to actually calculate the integral. [.", (c) If F(t) is an antiderivative of f(t), explain why the function F(t) is always increasing. (d) You are told that a total of 150mm of rain fell in May 2022. Using this fact draw a rough sketch of the antiderivative function F(t) of f(t) starting with F(0) = 0. Indicate any important aspects of the graph - maxima, minima, inflection points etc. (You do not need to find the formula for F(t) just make a rough sketch using what you know about f(t).) (e) If in (d) above you were given F(0) = 20, would that make a change to f(t) or not? If it does change f(t), explain how. If it does not change f(t), explain why not.
Transcribed Image Text:2. The function below, and its graph, gives the rainfall in mm/day that falls in the month of May, where t is measured in days and t = 0 coincides with 1 May 2022. f(t) = 50 t²20t + 101 (a) Showing all your calculations find the following: i. The day on which the rainfall was highest. ii. The day on which the rainfall per day was increasing the fastest. (b) What does the integral f(t)dt calculate? Explain clearly, but you do not need to actually calculate the integral. [.", (c) If F(t) is an antiderivative of f(t), explain why the function F(t) is always increasing. (d) You are told that a total of 150mm of rain fell in May 2022. Using this fact draw a rough sketch of the antiderivative function F(t) of f(t) starting with F(0) = 0. Indicate any important aspects of the graph - maxima, minima, inflection points etc. (You do not need to find the formula for F(t) just make a rough sketch using what you know about f(t).) (e) If in (d) above you were given F(0) = 20, would that make a change to f(t) or not? If it does change f(t), explain how. If it does not change f(t), explain why not.
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