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Math Help - Intro Calculus - Curve Sketching

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    Intro Calculus - Curve Sketching

    Sketch a graph of a function f(x) that is differentiable and that satisfies the following conditions.

    a) f'(x) > 0, when x < -3 and x > 1

    I don't know what to do... I'm used to sketching functions with equation questions and not interval questions....

    Please show me a step by step solution to this question, thanks
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    Moo
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    Hello,

    Quote Originally Posted by Macleef View Post
    Sketch a graph of a function f(x) that is differentiable and that satisfies the following conditions.

    a) f'(x) > 0, when x < -3 and x > 1

    I don't know what to do... I'm used to sketching functions with equation questions and not interval questions....

    Please show me a step by step solution to this question, thanks
    This means that in the part of the sketch where x<-3, the function will be increasing (derivative is positive). It will be the same for x>1.

    Between -3 and 1, the function is, for example, decreasing.
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    Quote Originally Posted by Moo View Post
    Hello,



    This means that in the part of the sketch where x<-3, the function will be increasing (derivative is positive). It will be the same for x>1.

    Between -3 and 1, the function is, for example, decreasing.
    Why is the section between -3 and 1 decreasing? Isn't it increasing since f'(x) is greater than 0?? I'm confused...
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    Moo
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    Quote Originally Posted by Macleef View Post
    Why is the section between -3 and 1 decreasing? Isn't it increasing since f'(x) is greater than 0?? I'm confused...
    You said it was increasing for x<-3, that is to say to the left of -3, and for x>1, that is to say to the right of 1.

    Between -3 and 1, you can choose
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    so it doesn't matter? would the graph look like a positive cubic function?
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    Quote Originally Posted by Macleef View Post
    so it doesn't matter? would the graph look like a positive cubic function?
    yeah, whatever... You're only asked that it increases in the given intervals.
    As the question is formulated, the function is just not increasing between -3 and 1 (so it can be constant or decreasing)
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    thanks for the help... and I read the question wrong... there's actually more to it than that...
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