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Math Help - Graphs and their Derivatives

  1. #1
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    Graphs and their Derivatives

    essentially, I am given different graphs, and the functions are not given. From the graph, i have to answer where the first derivative is positive or negative, where the second derivative is positive or negative, etc.

    I understand when the first derivative is positive and negative (when the gradient of the slope f(x) is positive or negative respectively). I dont understand when the second derivative is positive or negative, its confusing me. Can someone explain...? Thanks for your help.
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  2. #2
    Super Member 11rdc11's Avatar
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    Think about concavity and points of inflection
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  3. #3
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    Yep, for the second derivative, just look at where f'(x) is changing in concavity.
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  4. #4
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    so where f'(x) is negative is where f''(x) is positive?
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  5. #5
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    help

    This is the worksheet im currently doing.




    sorry its a bit big, and basically i am confused about what second derivative and first derivative measures.

    say for Question 2v , where is it negative? (i have the answers but don't know how to arrive at them)

    i also dont understand Q3ii and Q3 iii

    for question 4, f'(6) = 2, i dont know what this means.. and also i dont get Q4iv

    and i dont understand q5 and q6ii and q6iii

    Sorry, i have so many questions, but i need help, i have a test in 2 days... =[.
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  6. #6
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    please help im panicking...... just tell me how do i know where the second derivative is negative or positive by looking at the graph.
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  7. #7
    Super Member 11rdc11's Avatar
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    For intervals when f''(x)< 0 the function f(x) is concave down and for intervals when f''>0 the function f(x) is concave up.
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  8. #8
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    thanks i guess... but i already got help from somewhere else
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