Find the slope of the demand curve D(p) = 20 / sqrt (p-1), p>1, at point (5,10)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The demand slope is given by D(p) = 20 / sqrt (p - 1)

The slope of the curve is the value of the first derivative at the required point.

D(p) = 20 / sqrt (p - 1)

=> 20* ( p - 1)^(-1/2)

D'(p) = 20*(-1/2)*(p -1)^(-3/2)

At the point (5, 10), the slope is

D'(5) = -20*(1/2)*(5 -1)^(-3/2)

=> -20*(1/2)*(4)^(-3/2)

=> -20*(1/2)/8

=> -20/16

=> -1.25

The slope of the demand graph at (5, 10) is -1.25.

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