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The rate of working of an engine is given by f(v) = 15v + , 0 ≤ v ≤ 30, v unit being the speed of the engine. Then the value of v for which the rate of working is least, is

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  1. 20unit 
  2. 30 unit
  3. 40/3 unit
  4. 45/2 unit

Answer (Detailed Solution Below)

Option 1 : 20unit 
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Detailed Solution

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Given:

f(v) = 15v + 

Concept:

To find maxima and minima, 

Formula Used:

Calculation:

We have,

f(v) = 15v + 

⇒ R = 15v + 

On differentiating with respect to 'v'

⇒ 

⇒     ----- equation (1)

Again, differentiating with respect to 'v'

⇒      ----- equation (2)

For maximum or minimum, 

By substituting these values,

⇒ 

⇒ 

⇒ v2 = 

⇒ v2 = 400

⇒ v = 20 

⇒ 

⇒ 

⇒ 

⇒ v = 20 is the point of minimum.

∴ The rate of working of an engine is given by f(v) = 15v + , 0 ≤ v ≤ 30, v unit being the speed of the engine. Then the value of v for which the rate of working is least, is 20 unit.

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