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Friday, January 6

  1. page Practical tasks for determining the extreme values edited ... 2. Insert P'(a)=Derivative(P) to draw the first derivative of the function 3. Notice that whe…
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    2. Insert P'(a)=Derivative(P) to draw the first derivative of the function
    3. Notice that when a=4 (the x-coordinate of the point Extrem) and V=32m³ (the y-coordinate of the point Extrem) the area P has minimum value
    If the applet is not openning please click here
    Ex.6: The perimeter of an isosceles triangle is 24cm. A body in 3D is made with the rotation of the triangle around its base. How much should be the sides of the triangle, so that the 3D body has maximum volume?
    View online or download:  User Guide – solution with derivatives  
    GeoGebra Interactivity
    Directions For Interactivity
    1. Move the point of the slider a to change the length of the side a of the triangle
    2. Move the point of the slider b to change the length of the base of the traingle
    3. Move the point of the next slider to see step by step construction of the 3d body and calculate the volume
    4. Notice that when a=7cm,b=10cm or a=8cm,b=8cm or a=9cm,b=6cm or a=10cm,b=4cm or a=11cm,b=2cm an isosceles triangle with perimeter 24 sm can be constructed but the volume is maximum when a=9cm and b=6cm
    If the applet is not openning please click here
    View the Function of the Volume of the 3D body
    Directions For Interactivity
    1. Insert V(x) = 4x π (12 - x) and press on the Enter key to draw the Volume of the body V as a function of the base b of the triangle
    2. Insert V'(x)=Derivative(V) to draw the first derivative of the function
    3. Notice that when b=6 (the x-coordinate of the point Extreme) and V=452.39m³ (the y-coordinate of the point Extreme) the volume V has maximum value

    If the applet is not openning please click here
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