Question

If y = f(x) be the concave upward function and y = (x) be a function such that f'(x) g(x) . f(x) = x⁴ + 2x² + 10, then

(A)  g (x) has at least one root between two consecutive roots of f (x) = 0

(B)  g (x) has at most one root between two consecutive roots of f (x) = 0 

(C)  if α and β are two consecutive roots of f (x) = 0, then αβ <0 

(D)  when f (x) increases g (x) decreases

Answer 1

Correct option  (A, C)

Given that f (x) = cos(log x) ⇒ f(y) = cos(log y)

Therefore