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4 for all values of x. How large can f(3) possibly be? EXAMPLE 5Suppose that f(0) = -2 and f'(x) We are given that f is differentiable (and therefore continuous) everywhere. In particular, we can apply the SOLUTION Mean Value Theorem on the interval O, 31. There exists a number c such that ro(-0) f(3) (0) f(c) So f(3) f(0) f'(c) f'(c). =-2 + We are given that f'(x) s 4 for all x, so in particular we know that f'(c) Multiplying both sides of this inequality by 3, we have 3f'(c) So f(3) 2 f(c) s -2+ The largest possible value for f(3) is

4 for all values of x. How large can f(3) possibly be? EXAMPLE 5Suppose that f(0) = -2 and f'(x) We are given that f is differentiable (and therefore continuous) everywhere. In particular, we can apply the SOLUTION Mean Value Theorem on the interval O, 31. There exists a number c such that ro(-0) f(3) (0) f(c) So f(3) f(0) f'(c) f'(c). =-2 + We are given that f'(x) s 4 for all x, so in particular we know that f'(c) Multiplying both sides of this inequality by 3, we have 3f'(c) So f(3) 2 f(c) s -2+ The largest possible value for f(3) is

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter1: Functions
Section1.2: Functions Given By Tables
Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...
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4 for all values of x. How large can f(3) possibly be? EXAMPLE 5Suppose that f(0) = -2 and f'(x) We are given that f is differentiable (and therefore continuous) everywhere. In particular, we can apply the SOLUTION Mean Value Theorem on the interval O, 31. There exists a number c such that ro(-0) f(3) (0) f(c) So f(3) f(0) f'(c) f'(c). =-2 + We are given that f'(x) s 4 for all x, so in particular we know that f'(c) Multiplying both sides of this inequality by 3, we have 3f'(c) So f(3) 2 f(c) s -2+ The largest possible value for f(3) is
Transcribed Image Text:4 for all values of x. How large can f(3) possibly be? EXAMPLE 5Suppose that f(0) = -2 and f'(x) We are given that f is differentiable (and therefore continuous) everywhere. In particular, we can apply the SOLUTION Mean Value Theorem on the interval O, 31. There exists a number c such that ro(-0) f(3) (0) f(c) So f(3) f(0) f'(c) f'(c). =-2 + We are given that f'(x) s 4 for all x, so in particular we know that f'(c) Multiplying both sides of this inequality by 3, we have 3f'(c) So f(3) 2 f(c) s -2+ The largest possible value for f(3) is
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