the function, f(x)=15√x, is given. determine when the function is positive, negative, increasing, or…

Answer:

Positive: $(0,+\infty)$ Negative: None Increasing: $(0,+\infty)$ Decreasing: None End - behavior: $y\to+\infty$ as $x\to+\infty$

Explanation:

Step1: Analyze when positive

For $y = 15\sqrt{x}$, since $\sqrt{x}\geq0$ for $x\geq0$ and $15>0$, when $x>0$, $y>0$.

Step2: Analyze when negative

$\sqrt{x}\geq0$ and $15>0$, so $y = 15\sqrt{x}\geq0$ always, never negative.

Step3: Analyze increasing - decreasing

Take the derivative $y'=\frac{15}{2\sqrt{x}}>0$ for $x > 0$, so increasing on $(0,+\infty)$ and not decreasing anywhere.

Step4: Analyze end - behavior

As $x\to+\infty$, $\sqrt{x}\to+\infty$, and since $y = 15\sqrt{x}$, $y\to+\infty$.