Find the critical points and the intervals on which the function f(x) = x^4 - 2x^{3/2}, (x > 0) is increasing or decreasing. Use the First Derivative Test to determine whether the critical point is a local minimum or maximum (or neither). Find the x-coordinates of the critical points that correspond to a local minimum. (Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DNE if there are no critical points.) x = Find the x-coordinates of the critical points that correspond to a local maximum. (Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DNE if there are no critical points.) x = Find the intervals over which the function is increasing and decreasing. (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*,*). Use the symbol ? for infinity, ? for combining intervals, and an appropriate type of parenthesis "(", ")", "[" or "]" depending on whether the interval is open or closed. Enter Ø if interval is empty.) the function is increasing on
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To find the critical points, we need to find the values of x where the derivative of the function is equal to zero or undefined. Taking the derivative of f(x), we get: f'(x) = 4x^3 - 3x^(1/2) Setting f'(x) equal to zero, we have: 4x^3 - 3x^(1/2) = 0 To solve Show more…
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