Verify only that the velocity field for unidirectional fully

Verify (only) that the velocity field for unidirectional fully-developed, steady-state flow of a fluid of viscosity mu under a pressure-driven flow P(z = 0) = Pin, P(z = L) = P_out in a square duct, of length L and bordered by the lines x = plusminusD and

Solution

a) x-int :
Where does it meet x-axis?
It meets it at x = -3.8, x = -2 and x = 1.4
So, x-int are approx (-3.8 , 0) and (-2 , 0) and (1.4 , 0)

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b) y-int :
Where does it meet y-axis?
It meets it at y = 2.5
So, y-int is (0 , 2.5)

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c) Domain :
The range of x-values taken on by this function is the domain
Here, the domain is [-4 , 3]

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d) Range :
The max y-value is 3
The min y-value is -4
So, range is [-4 , 3]

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e) f(-3) :
When x = -3, what is y?
It is -2
So, f(-3) = -2

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f) Increasing :
The regions where when u view the function from left to right, the graph is going upward is where it is increasing.
So, increasing is : (-3 , 0)

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g) Decreasing :
Going downward
So, decreasing range is : [-4 , -3) U (0 , 3]