How do you find the maximum/minimum value of an equation?
When finding the maximum or minimum of an equation, make sure you rearrange an equation to make y the subject of the equation i.e. y=_________. You can then differentiate with respect to x and then set the differentiated equation to zero.
E.g. If y = 3x2 + 5, y' = 6x. Setting y' = 0, you will find that x is also 0. Substitute this back into the original equation:
y= 3(0)2 + 5 = 5, so therefore the minimum value is 5. To check if this is a maximum or a minimum value, differentiate it again and check if it is a positive value (therefore a minimum) or a negative value (therefore a maximum).
I.e. y'' = 6 which is positive, therefore is a minimum value.
You can check to see if this is true by drawing a graph. You should see a U shaped curve where bottom of the graph has the coordinates of (0,5).
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