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For minimizing the transfer function the condition is :
- a)Second differentiation of the function must be zero
- b)Second differentiation of the function must be positive
- c)Second differentiation of the function must be negative
- d)Second differentiation of the function must be complex
Correct answer is option 'C'. Can you explain this answer?
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For minimizing the transfer function the condition is :a)Second differ...
Explanation: In optimal control problems the main objective is to reduce the performance criterion which is used only when the second differentiation of the function must be negative.
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For minimizing the transfer function the condition is :a)Second differ...
Minimizing the Transfer Function
To minimize the transfer function, the second differentiation of the function must be negative. Let's understand why this condition is necessary for minimizing the transfer function.
Second Differentiation of the Function
When we take the second derivative of a function and it is negative, it implies that the function is concave down. In the context of minimizing a transfer function, a concave down function indicates that the function is reaching a minimum point. This means that the function is decreasing as we move towards the minimum.
Significance of Concave Down Function
In the process of minimizing a transfer function, we want to reach the point where the function has the lowest value. A concave down function helps us identify this minimum point as the function continues to decrease.
Alternative Options
- If the second differentiation of the function is zero, it indicates a point of inflection where the function neither increases nor decreases.
- If the second differentiation is positive, the function is concave up, which means it is increasing and not approaching a minimum.
- If the second differentiation is complex, it may introduce unnecessary complications in the minimization process.
Therefore, for minimizing the transfer function effectively, it is crucial that the second differentiation of the function is negative to ensure the function is concave down and approaching a minimum point.
To minimize the transfer function, the second differentiation of the function must be negative. Let's understand why this condition is necessary for minimizing the transfer function.
Second Differentiation of the Function
When we take the second derivative of a function and it is negative, it implies that the function is concave down. In the context of minimizing a transfer function, a concave down function indicates that the function is reaching a minimum point. This means that the function is decreasing as we move towards the minimum.
Significance of Concave Down Function
In the process of minimizing a transfer function, we want to reach the point where the function has the lowest value. A concave down function helps us identify this minimum point as the function continues to decrease.
Alternative Options
- If the second differentiation of the function is zero, it indicates a point of inflection where the function neither increases nor decreases.
- If the second differentiation is positive, the function is concave up, which means it is increasing and not approaching a minimum.
- If the second differentiation is complex, it may introduce unnecessary complications in the minimization process.
Therefore, for minimizing the transfer function effectively, it is crucial that the second differentiation of the function is negative to ensure the function is concave down and approaching a minimum point.
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For minimizing the transfer function the condition is :a)Second differentiation of the function must be zerob)Second differentiation of the function must be positivec)Second differentiation of the function must be negatived)Second differentiation of the function must be complexCorrect answer is option 'C'. Can you explain this answer?
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