AP EAMCET · Maths · Application of Derivatives
The maximum value of on is
- A
- B
- C
- D
Answer & Solution
Correct Answer
(C)
Step-by-step Solution
Detailed explanation
∵ fx=x4+x+x2 On differentiating w.r.t. x, we get f′x=4+x+x2-x(1+2x)4+x+x22 For maximum, put f′x=0 ⇒ 4-x24+x+x22=0 Given x∈[ −1, 1 ] ⇒ x 2 ∈[ 0, 1 ] ⇒4− x 2 >0 ⇒ f ′ ( x ) is increasing in [ −1, 1 ] and its maximum value will be f( 1 )= 1 6 .
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