Explanation Results used: Mean Value Theorem: “Let f be a function that satisfies the fsollowing hypothesis: 1. f is continuous on the closed interval [ a , b ] . 2. f is differentiable on the open interval ( a , b ) . Then, there is a number c in ( a , b ) such that f ′ ( c ) = f ( b ) − f ( a ) b − a . Or, equivalently, f ( b ) − f ( a ) = f ′ ( c ) ( b − a ) ”. Since it is given that 2 ≤ f ′ ( x ) ≤ 5 assume that the function is differentiable on (0,4). Also, it is given that f is continuous on [0,4]

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Author: Stewart

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Chapter 4, Problem 36RE

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To prove: For a continuous function f on [0,4] if f(0)=1 and 2≤f′(x)≤5 for all x in (0,4), 9≤f(4)≤21 .

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Chapter 4, Problem 35RE

Chapter 4, Problem 37RE

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To prove: For a continuous function f on [ 0 , 4 ] if f ( 0 ) = 1 and 2 ≤ f ′ ( x ) ≤ 5 for all x in (0,4), 9 ≤ f ( 4 ) ≤ 21 .

Solution Summary: The author proves that f is continuous on the closed interval left[a,bright].

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To prove: For a continuous function f on [0,4] if f(0)=1 and 2≤f′(x)≤5 for all x in (0,4), 9≤f(4)≤21 .

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Chapter 4 Solutions