In which interval is the function f(x) = x^3 | vedclass

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(A) To find the interval where the function $f(x) = x^3 + 5x^2 - 1$ is decreasing,we need to find the interval where its derivative $f'(x) < 0$.First,

Vedclass · Accepted Answer

$-\frac{10}{3} < x < 0$

Vedclass · Answer

(A) To find the interval where the function $f(x) = x^3 + 5x^2 - 1$ is decreasing,we need to find the interval where its derivative $f'(x) First,find the derivative of $f(x)$:$f'(x) = \frac{d}{dx}(x^3 + 5x^2 - 1) = 3x^2 + 10x$Now,set the derivative to be less than zero:$3x^2 + 10x Factor out $x$:$x(3x + 10) The critical points are $x = 0$ and $x = -\frac{10}{3}$.Using the sign scheme method,we test the intervals:For $x  0$.For $-\frac{10}{3} For $x > 0$,$f'(x) > 0$.Thus,the function is decreasing in the interval $(-\frac{10}{3}, 0)$.

In which interval is the function $f(x) = x^3 + 5x^2 - 1$ a decreasing function?

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