Assume that f ' (x)≤ M for a ≤ x ≤ b. One can show by the Mean ValueTheorem that f (b) − f (a) ≤ M (b − a), and thus f (a) − M(b − a) ≤ f(b) ≤ f (a) + M(b − a). Using this fact, determine a lower bound and an upper bound for 17^1/2 (Hint: Let f (x) = x^1/2, a = 16, and b = 17, and then find bounds for f (17) = 17^1/2.First, find a reasonable value for M:      M =  Then fill in the blanks:   ≤ f (17) ≤

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Asked Oct 9, 2019
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Assume that f ' (x)≤ M for a ≤ x ≤ b. One can show by the Mean Value
Theorem that f (b) − f (a) ≤ M (b − a), and thus f (a) − M(b − a) ≤ f(b) ≤ f (a) + M(b − a). Using this fact, determine a lower bound and an upper bound for 17^1/2 

(Hint: Let f (x) = x^1/2, a = 16, and b = 17, and then find bounds for f (17) = 17^1/2.

First, find a reasonable value for M:      M =  
Then fill in the blanks:   ≤ f (17) ≤  

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Expert Answer

Step 1

From the given information, f(x) = x1/2, a = 16 and b = 17, t...

Obtain the derivative of the function as given below
1
f(x)=
2
1
2/x
M for asx<b
From the given information assume that
That is, 16x<17
Substitute 16 for x in f (x) has the maximum value
1
f(16)216
1
= M
1
maximum at
Therefore, the derivative f (x) i
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Obtain the derivative of the function as given below 1 f(x)= 2 1 2/x M for asx<b From the given information assume that That is, 16x<17 Substitute 16 for x in f (x) has the maximum value 1 f(16)216 1 = M 1 maximum at Therefore, the derivative f (x) i

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