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

**EXERCISE 7.7**

**1. Find intervals of concavity and points of inflexion for the following functions:**

**(i) f (x) = x ( x âˆ’ 4)3**

**(ii) f (x) = sin x + cos x, 0 < x < 2Ï€**

**(iii) f (x) = 1/2 ( ex âˆ’ eâˆ’x )**

**2. Find the local extrema for the following functions using second derivative test :**

**(i) f (x) = âˆ’3x5 + 5x3**

**(ii) f (x) = x log x**

**(iii) f (x) = x2 eâˆ’2x**

**3. For the function f (x) = 4x3 + 3x2 âˆ’ 6x +1 find the intervals of monotonicity, local extrema, intervals of concavity and points of inflection.**

**Answers:**

**(1) (i) concave upwards on ( âˆ’âˆž, 2) and ( 4, âˆž) . Concave downwards on ( 2, 4)**

**Points of inflection ( 2, âˆ’16) and ( 4, 0)**

** (ii) concave upwards on . Concave downwards on **

**Points of inflection **

**(iii) concave upwards on ( 0, âˆž). Concave downward on ( âˆ’âˆž, 0) Points of inflection ( 0, 0)**

**(2) (i) local minimum = âˆ’2 ; local maximum = 2 (ii) local minimum = âˆ’ 1/e (iii) local minimum = 0 ; local maximum = 1/e2**

**(3) strictly increasing on (âˆ’âˆž, âˆ’1) and (1/2 , âˆž) . strictly increasing on (âˆ’1, 1/2) local maximum = 6 , local minimum = âˆ’ 3/4 concave downwards on (âˆ’âˆž, âˆ’1/4) ; concave upwards on (âˆ’ 1/4, âˆž) . point of inflection (âˆ’ 1/4, 21 /8)**

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 7.7: Applications of Second Derivative | Problem Questions with Answer, Solution

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