If f(x) = x^5 - 5x^4 + 5x^3 - 10 has local ma | vedclass

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(B) Given $f(x) = x^5 - 5x^4 + 5x^3 - 10$.Find the derivative: $f'(x) = 5x^4 - 20x^3 + 15x^2$.Set $f'(x) = 0$ to find critical points:$5x^2(x^2 - 4x +

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$(1, 3)$

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(B) Given $f(x) = x^5 - 5x^4 + 5x^3 - 10$.Find the derivative: $f'(x) = 5x^4 - 20x^3 + 15x^2$.Set $f'(x) = 0$ to find critical points:$5x^2(x^2 - 4x + 3) = 0$$5x^2(x - 1)(x - 3) = 0$Thus,the critical points are $x = 0, 1, 3$.Using the first derivative test:For $x  0$.For $0  0$.For $1 For $x > 3$,$f'(x) > 0$.At $x = 1$,the derivative changes from positive to negative,so $f(x)$ has a local maximum at $p = 1$.At $x = 3$,the derivative changes from negative to positive,so $f(x)$ has a local minimum at $q = 3$.Therefore,$(p, q) = (1, 3)$.

If $f(x) = x^5 - 5x^4 + 5x^3 - 10$ has local maximum and minimum at $x = p$ and $x = q$,respectively,then $(p, q)$ equals

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