NPTEL Data Science for Engineers Week 4 Assignment Answers 2025
1. Letf(x)=x3+3x2−24+7. Select the correct options from the following:
- x=2 will give the maximum for f(x).
- x=2 will give the minimum forf(x).
- Maximum value of f(x) is 87.
- The stationary points forf(x) are 2 and 4.
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2. Find the gradient of f(x)=x2y at (x,y)=(1,3).
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3. Find the Hessian matrix for f(x,y)=x2y at (x,y)=(1,3)
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4. Let f(x,y)=−3x2−6xy−6y2. The point (0, 0) is a
- saddle point
- maxima
- minima
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5.
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6. Consider f(x)=x3−12x−5 Which among the following statements are true?
- f(x) is increasing in the interval (−2,2).
- f(x) is increasing in the interval (2,∞)
- f(x) is decreasing in the interval (−∞,−2)
- f(x) is decreasing in the interval (−2,2)
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7.
Let x∗ be the maximizer of f(x). What is the second order sufficient condition for x∗ to be the maximizer of the function f(x)?
- 4x2+21x2+10x−17=0
- 12x2+42x+10=0
- 12x2+42x+10>0
- 12x2+42x+10<0
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8. In optimization problem, the function that we want to optimize is called
- Decision function
- Constraints function
- Optimal function
- Objective function
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9. The optimization problem minxf(x) can also be written as maxxf(x)
- True
- False
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10. Gradient descent algorithm converges to the local minimum
- True
- False
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