Question

The solution set of ƒ′(x) > g′(x) where ƒ(x) = (1/2)5^{2x + 1} and g(x) = 5^x + 4x log_e 5 is –

• A. (1, ∞)
• B. (0, 1)
• C. [0, ∞)
• D. (0, ∞)

Answer 1

Answer: (D)

(0, ∞)

Answer 2

$\left( \frac{1}{2} \right)$5^{2x + 1} log_e5 × 2 > 5^x log_e 5 + 4 log_e 5

⇒ 5^2x . 5 > 5^x + 4

⇒ 5 . 5^2x – 5^x – 4 > 0

⇒ (5^x – 1) (5.5^x + 4) > 0 Q 5^x > 1

∴ x > 0.