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Math Help - Graph sketch

  1. #1
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    Graph sketch

    Given:

    f(0)=f(2)=0
    f'(x) < 0 if  x < 1
    f'(1)=0
    f'(x) > 0 if x > 1
    f''(x) > 0

    How can I sketch a graph of the function f given these characteristics? How would it look and how can I prove this?
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by AMaccy View Post
    Given:

    f(0)=f(2)=0
    f'(x) < 0 if  x < 1
    f'(1)=0
    f'(x) > 0 if x > 1
    f''(x) > 0

    How can I sketch a graph of the function f given these characteristics? How would it look and how can I prove this?
    the curve intersect the x-axis at two points (0,0) and (2,0) and you have f'(1) is a critical point because f'(1)=0
    f is increasing in the interval x>1 (1,\infty ) and decreasing in the interval (-\infty , 1) and the curve is concave up for all values of x



    I think the curve is x^2-2x
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