Hello NPTEL Learners, In this article, you will find **NPTEL Data Science for Engineers Assignment 4 Week 4 Answers 2023**. All the Answers are provided below to help the students as a reference don’t straight away look for the solutions, first try to solve the questions by yourself. If you find any difficulty, then look for the solutions.

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## NPTEL Data Science for Engineers Assignment 4 Answers 2023:

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#### Q.1. Let f(x)=x3+6×2−3x−5 . 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.

Use the following information to answer Q2 and Q3.

Consider the following optimization problem:

maxxϵRf(x)max

, where

f(x)=x4+7×3+5×2−17x+3

Let x∗ be the maximizer of f(x)

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

#### Q.3. Find the value of x∗.

- -4.48
- 0.66
**-1.43**- 4.45

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#### Q.4. Let f(x)=2sinx,0≤x≤2π . Select the correct options from the following:

- π/2 is the global maximum of f(x).
**π is the global minimum of f(x).****3π/2 is the global maximum of f(x).**- 3π/2 is the global minimum of f(x).

Use the following information to answer Q5, Q6, Q7 and Q8.

Let f(x)=2×21+3x1x2+3×22+x1+3×2.

#### Q.5.** **Find the gradient for f(x).

**Answer:**A

#### Q.6. Find the stationary point for f(x).

#### Q.7. Find the Hessian matrix for f(x).

**Answer:**C

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#### Q.8. The stationary point obtained in Q6 is a

- maxima
**minima**- saddle point

#### Q.9. Let f(x1,x2)=4×21−4x1x2+2×22 . Select the correct options from the following:

- (2, 4) is a stationary point of f(x).
**(0, 0) is a stationary point of f(x).****The Hessian matrix ▽2f is positive definite.**- The Hessian matrix ▽2f is not positive definite.

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

#### Q.11. The optimization problem minxf(x) can also be written as maxxf(x) .

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

- True
**False**

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**Disclaimer**: This answer is provided by us only for discussion purpose if any answer will be getting wrong don’t blame us. If any doubt or suggestions regarding any question kindly comment. The solution is provided by **Chase2learn**. This tutorial is only for Discussion and Learning purpose.

#### About NPTEL Data Science for Engineers Course:

**Learning Objectives :**

- Introduce R as a programming language
- Introduce the mathematical foundations required for data science
- Introduce the first level data science algorithms
- Introduce a data analytics problem solving framework
- Introduce a practical capstone case study

**Learning Outcomes:**

- Describe a flow process for data science problems (Remembering)
- Classify data science problems into standard typology (Comprehension)
- Develop R codes for data science solutions (Application)
- Correlate results to the solution approach followed (Analysis)
- Assess the solution approach (Evaluation)
- Construct use cases to validate approach and identify modifications required (Creating)

**Course Outcome:**

**Week 1:**Course philosophy and introduction to R**Week 2:**Linear algebra for data science- 1. Algebraic view – vectors, matrices, product of matrix & vector, rank, null space, solution of over-determined set of equations and pseudo-inverse)
- 2. Geometric view – vectors, distance, projections, eigenvalue decomposition
**Week 3:**Statistics (descriptive statistics, notion of probability, distributions, mean, variance, covariance, covariance matrix, understanding univariate and multivariate normal distributions, introduction to hypothesis testing, confidence interval for estimates)**Week 4:**Optimization**Week 5:**1. Optimization- 2. Typology of data science problems and a solution framework
**Week 6:**1. Simple linear regression and verifying assumptions used in linear regression- 2. Multivariate linear regression, model assessment, assessing importance of different variables, subset selection
**Week 7:**Classification using logistic regression**Week 8:**Classification using kNN and k-means clustering

**CRITERIA TO GET A CERTIFICATE**:

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

**YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.**

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