**Unformatted text preview: **l maximum or a local
minimum? 1 Hung Nguyen Problem Set 11 Solution 4.2 Mean Value Theorem 4.3 How Derivatives Affect Graph GE 207C 6. How many real roots does the equation
4. If f (1) = 10 and f '( x ) ≥ 2 for 1 ≤ x ≤ 4 , how small
can f ( 4) possibly be? Assume f ( x ) is differentiable
everywhere.
Solution:
From the Mean Value Theorem
f (4) − f (1)
f ' ( x) ≥
⇒ f (4) = f (1) + 3 f ' (c )
3
And since f ' (c) ≥ 2 , then f (4) ≥ 10 + 3(2) = 16 5. If f is a contin...

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