## 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:

- x=2 will give the maximum for f(x).
- x=2 will give the minimum for f(x).
- Maximum value of f(x) is 87.
- The stationary points for f(x)are 2and 4.

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2.

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3.

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4. Let f(x,y)=−3x^{2}−6xy−6y^{2} . The point (0,0) is a

- saddle point
- maxima
- minima

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5.

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6. Consider f(x)=x^{3}−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.

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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 min_{x} f(x) can also be written as max_{x} f(x).

- True
- False

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10. Gradient descent algorithm converges to the local minimum.

- True
- False

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