# PROBLEM LINK:

* Author:* Bhagya Kamal Jain

*Jatin Yadav*

**Tester:***Bhagya Kamal Jain*

**Editorialist:**# DIFFICULTY:

MEDIUM

# PREREQUISITES:

Binary/Ternary Search, Calculus

# PROBLEM:

You are given a function f(x)=(x2+b∗x+c)/sin(x) find its minimum value in the interval 0<x<π/2

# QUICK EXPLANATION:

Binary Search over x in the range to find the root of it’s derivative. Or Apply ternary search to find the minimum value directly.

# EXPLANATION:

You may look at the graph to confirm that f(x) is convex in the interval. Though it is possible to prove it mathematically.

Observe that that the function *f(x)* is convex in the given interval.

Ie. Its derivative is strictly increasing in the given interval.

Find the root of *f’(x)* by applying Binary Search. Minimum value of the function occurs at this value.

Then output the value of *f(x)* for the given x.

# ALTERNATE EXPLANATION:

Apply ternary search,read about it here.

Refer to author’s solution for the same.