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Mathematics Question on Application of derivatives

The minimum of f(x)=(10−x2)f(x)=\sqrt{(10-x^2)} in the interval [−3,2][-3,2] is

A

4\sqrt4

B

6\sqrt6

C

11

D

00

E

10\sqrt10

Answer

11

Explanation

Solution

Given that:
f(x)=√(10−x2)f(x) = √ (10 − x^2)
So,
f(x)=(10−x2)f(x) = \sqrt{(10 − x^2)} is maximum when x2x^2 is maximum.
Then, for [-3,2]
f(x)=√(10−x2)f(x) = √ (10 − x^2) such that :
∴ minimum of f(x)=(10−9)f(x) = \sqrt{(10 − 9 )}
=1=1= \sqrt1 =1
So, the correct option is (C) : 1.