Subjects calculus

Decreasing Interval

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Decreasing Interval


1. The problem is to find the interval where the function $$y=\frac{1}{16}-x^{2}$$ is decreasing. 2. The first step is to find the derivative of the function to analyze its increasing/decreasing behavior. The derivative is $$y'=0 - 2x = -2x$$. 3. The function is decreasing where its derivative is negative, i.e., $$y'<0$$. Set inequality: $$-2x < 0$$. 4. Solve for $$x$$: Dividing both sides by -2 (note: sign changes because dividing by negative) $$x > 0$$. 5. Therefore, the function is decreasing for $$x > 0$$. Final answer: The function $$y=\frac{1}{16} - x^{2}$$ is decreasing on the interval $$(0, \infty)$$.