Explanation
1. Understand the Property of Odd Functions
A function f(x) is said to be an odd function if:
2. Differentiate the Identity
To find the relationship between the derivatives, we differentiate both sides of the identity with respect to x using the Chain Rule:
3. Simplify the Derivative Relation
Multiplying both sides by −1, we get:
(Note: This shows that the derivative of an odd function is an even function.)
4. Substitute the Given Value
We are given that f′(3)=−2. To find f′(−3), we substitute x=3 into our derived relation:
Since f′(3)=−2:
Correct Option: (c) -2
