If and , where then in this interval
is an increasing function
Explanation for the correct answer:
Step 1: Solve for the first order derivative of and apply condition for increasing / decreasing function
A function is said to be increasing if in that interval and decreasing if in that interval
Consider
Differentiating with respect to we get
In the interval and
Hence,
Hence, is an increasing function in
Step-2: Solve for the first order derivative of
Consider
Differentiating with respect to we get
Let
Step- 3: Apply the condition for increasing/ decreasing function for and further conclude about
Differentiating with respect to we get
In the interval ,
is a decreasing function in the interval
Hence, is a decreasing function in the interval . So, option (C) is the correct answer.