Graph the Equation $y=x+\cos 2 x, 0 \leq x \leq \pi$

question 304

Multiple Choice

Graph the equation. Include the coordinates of any local and absolute extreme points and inflection points.
- $y=x+\cos 2 x, 0 \leq x \leq \pi$

• A) local minimum: \( \left(\frac{\pi}{4},-1\right) \) local maximum: \( \left(\frac{3 \pi}{4}, 3\right) \) inflection point: \( \left(\frac{\pi}{2}, 1\right) \)
• B) local minimum: \( (1.444,-0.246) \) local maximum: \( (0.126,1.031) \) inflection points: \( (0.785,0.393),(2.356,1.178 \)
• C) no local extrema inflection point: \( \left(\frac{\pi}{2}, \frac{\pi}{2}\right) \)
• D)local minimum: \( \left(\frac{5 \pi}{12}, \frac{5 \pi-6 \sqrt{3}}{12}\right) \) local maximum: \( \left(\frac{\pi}{12}, \frac{\pi+6 \sqrt{3}}{12}\right) \) inflection points: \( \left(\frac{\pi}{4}, \frac{\pi}{4}\right),\left(\frac{3 \pi}{4}, \frac{3 \pi}{4}\right) \)

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Definitions:

Electrolyte imbalance

A condition where the levels of electrolytes (minerals such as potassium, sodium, and calcium) in the body are either too high or too low, affecting bodily functions.

Leukemia

A medical condition in which bone marrow produces a large number of white blood cells that are not normal.

Potassium

A chemical element with symbol K, essential for life, particularly for heart function and muscle contraction.

Normal range

The set of values that is considered healthy and typical for a specific measurement in medicine, outside of which may signify disease or an abnormal condition.