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

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(B) Given $f(x) = x^5 - 5x^4 + 5x^3 - 10$.To find the local maxima and minima,we find the first derivative $f'(x)$:$f'(x) = 5x^4 - 20x^3 + 15x^2 = 5x^

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$(1, 3)$

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(B) Given $f(x) = x^5 - 5x^4 + 5x^3 - 10$.To find the local maxima and minima,we find the first derivative $f'(x)$:$f'(x) = 5x^4 - 20x^3 + 15x^2 = 5x^2(x^2 - 4x + 3) = 5x^2(x - 1)(x - 3)$.Setting $f'(x) = 0$,we get critical points $x = 0, 1, 3$.Now,we analyze the sign of $f'(x)$ around these points:For $x  0$.For $0  0$.For $1 For $x > 3$,$f'(x) > 0$.Since $f'(x)$ changes sign from positive to negative at $x = 1$,$x = 1$ is a point of local maximum $(p = 1)$.Since $f'(x)$ changes sign from negative to positive at $x = 3$,$x = 3$ is a point of local minimum $(q = 3)$.Thus,$(p, q) = (1, 3)$.

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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