Quiz Question - Calculus and Differential Equations

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2022-007

The Fermat Teorem defines that if f had a local maximum or minimum in c, and if f'(c) exists, then f'(c) = 0. A critical number of the function f is a number c in the domain of f where f'(c) = 0 or f'(c) does not exist.

Choose the statement that presents the critical numbers of \(f(x)=x^{3/5}(4-x)\).

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1. 0 and \({2/3}\)
2. \({2/3}\) and \({4/3}\) 
3. \({4/3}\) and \({3/2}\)
4. 0 and \({3/2}\)
5. None of the above.

Original idea by: Rubens de Castro Pereira