## NPTEL Data Science For Engineers Week 4 Assignment Answers 2024

1. Let f(x)=x^{3}+3x^{2}−24x+7. Select the correct options from the following:

- −2+√5 will give the maximum for f(x).
- −2+√5 will give the minimum for f(x).
- The stationary points for f(x) are −2+√5 and −2−√5.
- The stationary points for f(x) are −4 and 0.

Answer :-c

2. What is the second order sufficient condition for x^{∗} to be the maximizer of the function f(x) ?

- 4x
^{3}+21x^{2}+10x−17=0 - 12x
^{2}+42x+10=0 - 12x
^{2}+42x+10>0 - 12x
^{2}+42x+10<0

Answer :- d

3. Find the value of x^{∗}

- −4.48
- 0.66
- −1.43
- 4.45

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4.

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5.

Answer :-

6. Find the stationary point for f(x1, x2)

- 0.6, 0.4
- −0.6, −0.4
- 0.2, −0.6
- 0.2, 0.6

Answer :-

7.

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8. The stationary point obtained in the previous question is

- maxima
- minima
- saddle point

Answer :-

9.

Answer :-

10. In optimization problem, the function that we want to optimize is called

- Decision function
- Constraints function
- Optimal function
- Objective function

Answer :-

11. The optimization problem min_{x}f(x) can also be written as max_{x}f(X)

- True
- False

Answer :-

12. In the gradient descent algorithm, the step size should always be same for each iteration.

- True
- False

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