f(x) = e2x – (a + 1)ex + 2x is monotonic increasing for all... | MATH - INCREASING AND DECREASING FUNCTION | SolveeIt | Solveeit

Today, August 19

Question

f(x) = e^2x – (a + 1)e^x + 2x is monotonic increasing for all xÎR is

A

(3, 4)

B

(– ¥, 0)

C

(– ¥, 3]

D

(3, ¥)

Answer

(– ¥, 3]

Explanation

Solution

f ¢(x) = 2e^2x + (a + 1)e^x + 2 ³ 0 " xÎR

i.e. $2\left( e^{x} + \frac{1}{e^{x}} \right)$ – (a + 1) ³ 0 " xÎR

̃ 4 – (a + 1) ³ 0 or a £ 3