y = x³ + 7\non which intervals is this function decreasing?\na ∅\nb (-∞, ∞)\nc (-∞, 0) and (0, ∞)\nd (-∞…

y = x³ + 7\non which intervals is this function decreasing?\na ∅\nb (-∞, ∞)\nc (-∞, 0) and (0, ∞)\nd (-∞, -7) and (0, ∞)\ne (-∞, -7) and (-7, ∞)

y = x³ + 7\non which intervals is this function decreasing?\na ∅\nb (-∞, ∞)\nc (-∞, 0) and (0, ∞)\nd (-∞, -7) and (0, ∞)\ne (-∞, -7) and (-7, ∞)

Answer

Explanation:

Step1: Find the derivative

Differentiate $y = x^{3}+7$ using the power - rule. The derivative $y'=3x^{2}$.

Step2: Determine where the function is decreasing

A function is decreasing when $y'<0$. But for $y' = 3x^{2}$, since $x^{2}\geq0$ for all real $x$ and $3>0$, then $y'=3x^{2}\geq0$ for all real $x$. The only time $y' = 0$ is when $x = 0$, but there are no intervals where $y'<0$.

Answer:

A. $\varnothing$