Definite Integration

Section: Mathematics

Question : 14 of 46

Marks: +1, -0

Let b be a nonzero real number. Suppose f : R → R is a differentiable function such that f(0) = 1. If the derivative f' of f satisfies the equation
f′(x)=

f(x)

b2+x2

for all x ∈ R , then which of the following statements is/are TRUE?

[JEE Adv 2020 P2]

If b > 0, then f is an increasing function
If b < 0, then f is a decreasing function
f(x)f(–x) = 1 for all x ∈ R
f(x) – f(–x) = 0 for all x ∈ R

Validate

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