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Q.36 to 65 (Two marks Questions)
Q. Consider the function f(x) = 2x3 -3x2 in the domain [-1, 2]. The global minimum of f(x) is ____
(Important - Enter only the numerical value in the answer)
Correct answer is '-5'. Can you explain this answer?
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Q.36 to 65 (Two marks Questions)Q.Consider the function f(x) = 2x3-3x2...
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Q.36 to 65 (Two marks Questions)Q.Consider the function f(x) = 2x3-3x2...
Global Minimum of f(x) = 2x^3 - 3x^2 in the domain [-1, 2]
To find the global minimum of the given function f(x) = 2x^3 - 3x^2 in the domain [-1, 2], we need to analyze the critical points and endpoints of the function within the given domain.
To find the critical points, we need to find the values of x where the derivative of the function is equal to zero or undefined.
The derivative of f(x) is obtained by differentiating each term of the function with respect to x:
f'(x) = d/dx (2x^3) - d/dx (3x^2)
= 6x^2 - 6x
Next, we set f'(x) = 0 and solve for x:
6x^2 - 6x = 0
6x(x - 1) = 0
So, the critical points are x = 0 and x = 1.
The given domain is [-1, 2], which means we need to evaluate the function at x = -1 and x = 2 as well.
f(-1) = 2(-1)^3 - 3(-1)^2
= -2 - 3
= -5
f(2) = 2(2)^3 - 3(2)^2
= 16 - 12
= 4
Now, we compare the values of the critical points and endpoints to find the global minimum.
f(0) = 2(0)^3 - 3(0)^2
= 0
f(1) = 2(1)^3 - 3(1)^2
= 2 - 3
= -1
We can see that the minimum value of f(x) within the given domain is -5, which occurs at x = -1.
Therefore, the global minimum of f(x) = 2x^3 - 3x^2 in the domain [-1, 2] is -5.
To find the global minimum of the given function f(x) = 2x^3 - 3x^2 in the domain [-1, 2], we need to analyze the critical points and endpoints of the function within the given domain.
- Finding the critical points:
To find the critical points, we need to find the values of x where the derivative of the function is equal to zero or undefined.
The derivative of f(x) is obtained by differentiating each term of the function with respect to x:
f'(x) = d/dx (2x^3) - d/dx (3x^2)
= 6x^2 - 6x
Next, we set f'(x) = 0 and solve for x:
6x^2 - 6x = 0
6x(x - 1) = 0
So, the critical points are x = 0 and x = 1.
- Finding the endpoints:
The given domain is [-1, 2], which means we need to evaluate the function at x = -1 and x = 2 as well.
f(-1) = 2(-1)^3 - 3(-1)^2
= -2 - 3
= -5
f(2) = 2(2)^3 - 3(2)^2
= 16 - 12
= 4
- Comparing the values:
Now, we compare the values of the critical points and endpoints to find the global minimum.
f(0) = 2(0)^3 - 3(0)^2
= 0
f(1) = 2(1)^3 - 3(1)^2
= 2 - 3
= -1
We can see that the minimum value of f(x) within the given domain is -5, which occurs at x = -1.
Therefore, the global minimum of f(x) = 2x^3 - 3x^2 in the domain [-1, 2] is -5.
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Q.36 to 65 (Two marks Questions)Q.Consider the function f(x) = 2x3-3x2 in the domain [-1, 2]. The global minimum of f(x) is ____(Important - Enter only the numerical value in the answer)Correct answer is '-5'. Can you explain this answer?
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Q.36 to 65 (Two marks Questions)Q.Consider the function f(x) = 2x3-3x2 in the domain [-1, 2]. The global minimum of f(x) is ____(Important - Enter only the numerical value in the answer)Correct answer is '-5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Q.36 to 65 (Two marks Questions)Q.Consider the function f(x) = 2x3-3x2 in the domain [-1, 2]. The global minimum of f(x) is ____(Important - Enter only the numerical value in the answer)Correct answer is '-5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.36 to 65 (Two marks Questions)Q.Consider the function f(x) = 2x3-3x2 in the domain [-1, 2]. The global minimum of f(x) is ____(Important - Enter only the numerical value in the answer)Correct answer is '-5'. Can you explain this answer?.
Q.36 to 65 (Two marks Questions)Q.Consider the function f(x) = 2x3-3x2 in the domain [-1, 2]. The global minimum of f(x) is ____(Important - Enter only the numerical value in the answer)Correct answer is '-5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Q.36 to 65 (Two marks Questions)Q.Consider the function f(x) = 2x3-3x2 in the domain [-1, 2]. The global minimum of f(x) is ____(Important - Enter only the numerical value in the answer)Correct answer is '-5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.36 to 65 (Two marks Questions)Q.Consider the function f(x) = 2x3-3x2 in the domain [-1, 2]. The global minimum of f(x) is ____(Important - Enter only the numerical value in the answer)Correct answer is '-5'. Can you explain this answer?.
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