Math  /  Calculus

QuestionConsider the function f:RRf: \mathbf{R} \rightarrow \mathbf{R} defined by f(x)=x3(1x)5f(x)=x^{3}(1-x)^{5} (a) Provide a list of all the critical numbers of ff. Separate the values by a semi-colon should there be more than one. Input the word "none" (without quotes or capitals) should there be none. x=x= \square (b) Provide a list of all the local minima of ff (following the same instruction). x=x= \square (c) Provide a list of all the local maxima of ff (following the same instruction). x=x=\square

Studdy Solution
List the local maxima.
Local maxima occur at x=0;1 x = 0; 1 .
(a) Critical numbers: x=0;1;38 x = 0; 1; \frac{3}{8}
(b) Local minima: x=38 x = \frac{3}{8}
(c) Local maxima: x=0;1 x = 0; 1

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