Determine whether there exist any values of x in the interval [0, 2𝜋) such that the rate of change of f(x) = sec x and the rate of change of g(x) = csc x are equal.

Question

Determine whether there exist any values of x in the interval [0, 2𝜋)

 such that the rate of change of f(x) = sec x

 and the rate of change of g(x) = csc x

 are equal. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

x =

Answer 1

f'(x) = g'(x); secxtanx = - cscxcotx; (tanxsecx)² = - 1 (contradiction). So, such a value of x does not exist .