Sunday, 15 June 2014

Differentiation - Maximum and Minimum

The gradient at the maximum and minimum point is 0. Thus, to find maximum and minimum, these are the steps required.

Step 1: If you need to find maximum or minimum value of V, you first need an equation involving V.
Step 2: Differentiate the equation, to find e.g. dV/dx.
Step 3: Equate dV/dx to 0, and find x.
Step 4: Substitute x into equation of V (from step 1) to find the stationary value of V.
Step 5: To determine maximum or minimum, differentiate dV/dx to find d2V/dx2. Substitute in x from step 4.
If d2V/dx2 > 0, V is minimum.
If d2V/dx< 0, V is maximum.

Example question:
Find the maximum volume of the tank, if its volume, V, is given by the following equation:


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