Maths Book back answers and solution for Exercise questions - Mathematics : Applications of Differential Calculus: Applications of First Derivative: Problem Questions with Answer, Solution

**EXERCISE 7.6**

** **

**1. Find the absolute extrema of the following functions on the given closed interval.**

**(i) f ( x ) = x 2 âˆ’12x +10 ; [1, 2]**

**(i) f ( x ) = 3x4 âˆ’ 4x3 ; [âˆ’1, 2]**

**(i) f (x) = 6x4/3 âˆ’3x1/3 ; [âˆ’1, 1]**

**(iv) f (x) = 2 cos x + sin 2x ; [0, Ï€/2]**

**2. Find the intervals of monotonicities and hence find the local extremum for the following functions:**

**(i) f (x) = 2x3 + 3x2 âˆ’12x â€ƒ**

**(ii) f (x) = x / x âˆ’ 5**

**(iii) f (x) = ex / 1-x3**

**(iv) f (x) = ex/3 âˆ’ log x**

**(v) f (x) = sin x cos x + 5, x âˆˆ(0, 2Ï€ )**

**Answers:**

**(1)**

**(i) absolute maximum = âˆ’1 , absolute minimum = âˆ’26**

**(ii) absolute maximum = 16 , absolute minimum = âˆ’1**

**(iii) absolute maximum = 9 , absolute minimum = âˆ’ 9/8**

**(iv) absolute maximum = 3âˆš3 / 2 , absolute minimum = 0**

**(2)**

**(i) strictly increasing on ( -âˆž, 2 ) and (1,âˆž) , strictly decreasing on (âˆ’2,1)**

**local maximum = 20**

**local minimum = âˆ’7**

**(ii) strictly decreasing on ( âˆ’âˆž, 5) and (5, âˆž) . No local extremum.**

**(iii) strictly increasing on ( âˆ’âˆž, âˆž). No local extremum.**

**(iv) strictly decreasing on ( 0,1) , strictly increasing on (1, âˆž). local minimum = 1/3**

**(v) strictly increasing on **

**strictly decreasing on , . local maximum= 11/2 at x = Ï€ / 4, 5Ï€ /4.**

**local minimum= 9/2 at x = 3Ï€ / 4, 7Ï€ / 4.**

Tags : Problem Questions with Answer, Solution , 12th Maths : UNIT 7 : Applications of Differential Calculus

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12th Maths : UNIT 7 : Applications of Differential Calculus : Exercise 7.6 : Applications of First Derivative | Problem Questions with Answer, Solution

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