Find the critical points of f(x)= x^(3/4)−3x^(1/4)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The critical points of a function f(x) are those where f'(x) = 0

The function f(x)= `x^(3/4)-3x^(1/4)`

f'(x) = `(3/4)*x^(-1/4) - 3*(1/4)*x^(-3/4)`

=> `(3/4)(x^(-1/4) - x^(-3/4))`

=> `(3/4)(sqrt x - 1)/x^(3/4)`

Solving f'(x) = 0

=> `(3/4)(sqrt x - 1)/x^(3/4) = 0`

=> x = 1

The critical point of the function f(x) = `x^(3/4)-3x^(1/4)`   is at x = 1.

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