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Math Help - Applications of Differentiation

  1. #1
    Senior Member topher0805's Avatar
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    Applications of Differentiation

    Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below.

    ____________ ≤ f(6) - f(2) ≤ ____________
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  2. #2
    Moo
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    Hello,

    Is that all you have ?
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    Quote Originally Posted by topher0805 View Post
    Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below.

    ____________ ≤ f(6) - f(2) ≤ ____________
    f(6)-f(2) = f'(c)(6-2)\implies 16\leq f(6)-f(2)\leq 20. By the Mean Value Theorem.
    (Here c\in (2,6)).
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    Senior Member topher0805's Avatar
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    Thanks for the help.

    Just to clarify, since 6-2 is 4, you multiplied both sides of the original inequality by 4 so that you had f(6)-f(2) by itself in the middle?
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    Quote Originally Posted by topher0805 View Post
    Thanks for the help.

    Just to clarify, since 6-2 is 4, you multiplied both sides of the original inequality by 4 so that you had f(6)-f(2) by itself in the middle?
    Exactly. you are on your way to be a math professor.
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