The application problem chosen for this discussion is y=(x2 -4x-1)/x
For what values of the independent variable does the function have a practical
interpretation in the context of your application problem? Explain.
In my independent variables, x should be greater than 0. This is important because it facilitates
practical interpretation.
In Desmos, draw the graph of the first derivative function and interpret it in the context of
your application problem.
2) given;
!
y=x?4?”
!
First derivative: y?=1+” !
graph of first derivative (y’):
Find all values, for which the first derivative of the function is 0 and interpret them in the
context of your application problem
When the rate of x is increased, the y decreases. From my application problem, there is no value
of x whereby the first derivative of the function is 0.
In Desmos, draw the graph of the second derivative function and interpret it in the context
of your application problem.
4) second derivative:
!
y??=? “? ”
With increasing of x, rate of change of y’ increases.
From the graph, the increase in x lead to increase in the change of y The second derivative is
mostly 0 whereas x tends to be infinity. This means the number of goods denoted by x tends to
be a huge quantity while the change rate of y becomes 0.

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