CALCULUS
CALCULUS
11th Edition
ISBN: 9780357092477
Author: Larson
Publisher: Cengage
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 1.4, Problem 128E

(a)

To determine

To Prove: f1(c) =f2(c)  if f1(x)  and f2(x)  be continuous functions on closed interval [a, b] and f1(a)<f2(a), f1(b)>f2(b)

b)

To determine

To Prove: There exists c in [0, π2] such that cosx=x and approximate the value of c to three decimal points by using graphing utility.

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Chapter 1 Solutions

CALCULUS

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