The critical numbers of the function F(x) = x^(4/5) (x - 4)^(2) are determined by finding the values of x that make the derivative F'(x) equal to zero. The derivative simplifies to (1 / 5th root of x) (x - 4)(2x + 4/5(x - 4)). To find critical values, set each factor of the derivative to zero: 1) 5th root of x = 0, 2) x - 4 = 0, and 3) 2x + 4/5(x - 4) = 0. Solving these equations yields the critical numbers necessary for further analysis.
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You're almost there. What values of x make F'(x) = 0? You have three factors, so for F'(x) to be zero, at least one of the factors must be zero.TsAmE said:Homework Statement
Find the critical numbers of the function:
F(x) = x^(4/5) (x - 4)^(2)
Homework Equations
None.
The Attempt at a Solution
I differentiated and got to (1 / 5th root of x) (x - 4)(2x + 4/5(x-4))
but I don't know how I can simplify the expression to be able to solve for the critical values of x