Equations without stationary points

Given y = 4/√(2x-3), x > 1.5

(a)Find dy/dx

(b)Explain why the graph of y = 4/√(2x – 3) does not have a stationary point

(c)State whether y = 4√(2x – 3) is an increasing or decreasing function. Explain your answer clearly.

y = 4(2x – 3)-1/2

dy/dx = -2(2x – 3)-3/2(2)

           = -4(2x – 3)-3/2

(b) Since, dy/dx = -4(2x – 3)-3/2  , (2x-3) is always positive

     (2x – 3 )-3/2 > 0

  • dy/dx < 0, dy/dx ≠ 0, therefore graph has no stationary point

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