Question

Let f: ℝ → ℝ be a solution of the differential equation
$\frac{d^2y}{dx^2}-2\frac{dy}{dx}+y=2e^x$ for x ∈ $\R$.
Consider the following statements.
P : If f(x) > 0 for all x ∈ ℝ, then f'(x) > 0 for all x ∈ ℝ.
Q : If f'(x) > 0 for all x ∈ ℝ, then f(x) > 0 for all x ∈ ℝ.
Then, which one of the following holds ?

• A. P is true but Q is false
• B. P is false but Q is true
• C. Both P and Q are true
• D. Both P and Q are false

Answer 1

Answer: (B)

P is false but Q is true

Answer 2

The correct option is (B) : P is false but Q is true.