Most Important Selected Qs for JEE AdvancedMathematicsIndefinite Integration

f(x)= x^8+4 x^4-2 x^2+2 d x and f(0)=0 , then

Options

Af ( x ) is an odd function
Bf(x) has range R
Cf(x) has at least one rela root
Df(x) is a monotonic function

Correct answer

D. f(x) is a monotonic function

Step-by-step solution

f(x)= x^8+4 x^4-2 x^2+2 d x, f(0)=0= x^8+4+4 x^4-4 x^4 x^4-2 x^2+2 d x= (x^4+2 x^2+2 ) (x^4-2 x^2+2 ) (x^4-2 x^2+2 ) d x= x^5 5 + 2 3 x^3+2 x+cf(0)=0+c=0 c=0 f(x)= x^5 5 + 2 x^3 3 +2 x f(x) is an odd function, its range is R , has at least one real root, is monotonic

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