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Math Help - Understanding A Function using its derivative?

  1. #1
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    Understanding A Function using its derivative?

    Hey guys. Can you please help me with this.

    A test question states that f'(x) \leqslant 5 for all values of x, and that f(0) = -3. What is the maximum possible value for f(4)?

    What in god's name do I do? I understand that it means that the slope of f is never bigger than 5 but that's it. It has to do with applying mean value thereom
    Last edited by RezMan; May 7th 2011 at 10:56 PM.
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  2. #2
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    Quote Originally Posted by RezMan View Post
    Hey guys. Can you please help me with this.

    A test question states that f'(x) \leqslant 5 for all values of x, and that f(0) = -3. What is the maximum possible value for f(4)?

    What in god's name do I do? I understand that it means that the slope of f is never bigger than 5 but that's it.
    1. Consider a straight line passing through (0, -3) with a slope of m = 5. It's equation is:
    y = 5x-3

    2. According to the text of the question the graph of f is always below this line or is this line. So the utmost value of f at x = 4 is: 5*4 - 3 = 17
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  3. #3
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    oh my god you're right! I found to do it this way: 5 \geqslant \frac{f(4)+3}{4-0}
    20  \geqslant f(4)+3
    17  \geqslant f(4)

    thank you so much. Since this was a silly little problem should I remove it from the board?
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