Question

Let f(x) = cos(x) and g(x) =$1-\frac{x^2}{2}$ for $x \in (-\frac{\pi}{2},\frac{\pi}{2})$. Then

• A. f(x) ≥ g(x) for all $x \in (-\frac{\pi}{2},\frac{\pi}{2})$
• B. f(x) ≤ g(x) for all $x \in (-\frac{\pi}{2},\frac{\pi}{2})$
• C. f(x) − g(x) changes sign exactly once on $(-\frac{\pi}{2},\frac{\pi}{2})$
• D. f(x) − g(x) changes sign more than once on $(-\frac{\pi}{2},\frac{\pi}{2})$

Answer 1

Answer: (A)

f(x) ≥ g(x) for all $x \in (-\frac{\pi}{2},\frac{\pi}{2})$

Answer 2

The correct option is (A) : f(x) ≥ g(x) for all $x \in (-\frac{\pi}{2},\frac{\pi}{2})$.