Question

Let f(x) be a second degree polynomial function such that ln (f(x)) > 0 " x Ī R and the equation f '(x) + 21 f(x) = 0 has no real roots. If g(x) = e^21x f(x). Then

• A. G(x) is an increasing function
• B. G(x) is an even function
• C. G(x) is a decreasing function
• D. The graph of g(x) cuts x-axis exactly once

Answer 1

Answer: (A)

G(x) is an increasing function

Answer 2

ln f(x) > 0 Ž f(x) > 1

f '(x) + 21 f(x) > 0 " x Ī R

Ž e^21x f '(x) + 21 e^21x f(x) > 0 " x Ī R

Ž $\frac{d}{dx}$ (f(x) e^21x) > 0 " x Ī R

Ž g(x) is an increasing function