Exam 1

  1. Question

    A graph of the function y=F(x)y=F(x) is provided below.

    Select each of the true statements from the following:


    1. F(4)>0F^'(-4) > 0
    2. F(3)=0F^'(-3) = 0
    3. F(3)=0F(-3) = 0
    4. All of the above statements are false.

    Solution

    1. True. The derivative of F(x)F(x) is positive when x<3x<-3, that is when the graph of F(x)F(x) is increasing. The derivative of F(x)F(x) is negative when x>3x>-3, that is when the graph of F(x)F(x) is decreasing. The derivative of F(x)F(x) is zero when x=3x=-3, that is when the graph of F(x)F(x) changes from increasing to decreasing or from increasing to decreasing. The derivative of F(x)F(x) is also zero when the graph of F(x)F(x) is constant (i.e., a line with zero slope.)
    2. True. The derivative of F(x)F(x) is zero when x=3x=-3, that is when the graph of F(x)F(x) changes from increasing to decreasing or from increasing to decreasing.
    3. True. F(3)=0F(-3) = 0, since the point (3,0)(-3,0) is on the graph of F(x)F(x)
    4. False.