We can go through options for this question

Option a is wrong because 0 is not included in (-π,0)

At x = -π/4 value of f(x) is -√2 = -1.41

At x = -π/3 value of f(x) is -2.

At x = -π/2 value of f(x) is -1.

∴ f(x) has max value at x =-π/2.

Which is -1.