## EXPERT ANSWER

In this question given in above figure we use the first derivative test to find relative maximum and minimum.

If the derivative f’ (x) changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point. … When this technique is used to determine local maximum or minimum function values, it is called the First Derivative Test for Local Extrema.

Here at x=4 the derivative changes from -ve to + ve so at this point f(x) has relative minima.

at x=6 the derivative changes from +ve to -ve so at this point f(x) has relative Maxima.

Option (C) is correct.

The function f(x) has relative minima at x=4 and relative maxima at x=6.