Question 18
Let the f : R β R be defined by f (x) = 2x + cos x, then f :
(A) has a minimum at x = π (B) has a maximum, at x = 0
(C) is a decreasing function (D) is an increasing function
Given
f (π) = 2π + cos π
Since we need to check
If it is increasing or decreasing
Or, at what value of π₯ the function has maximum or minimum value
Thus, we check sign of πβ²(π)
β΄ Differentiating π(π₯) w.r.t. π₯
f (π₯) = 2π₯ + cos π₯
fβ (π) = 2 β sin π
Checking sign of πβ²(π)
We know that
β1 β€ sin π β€ 1
Multiplying by β1
β1 Γ (β1) β₯ βsin π₯ β₯ 1 Γ (β1)
1 β₯ β sin π₯ β₯ β1
β1 β€ β sin π β€ 1
Adding 2 both sides
2 β 1 β€ 2 β sin π₯ β€ 2 + 1
1 β€ 2 β sin π β€ 3
1 β€ πβ²(π)β€ 3
β΄ πβ²(π) > 0
Thus, f (π₯) is increasing function
So, the correct answer is (D)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!