NPTEL Data Science For Engineers Week 4 Assignment Answers 2023

NPTEL Data Science For Engineers Week 4 Assignment Answers

NPTEL Data Science For Engineers Week 4 Assignment Answers 2023

1. Let f(x)=x3+3×2−24x+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 2 and 4.

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2. Find the gradient of f(x,y)=x2y at (x,y)=(1,3) .

∇f=[16]
∇f=[61]
∇f=[69]
∇f=[33]

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3. Find the Hessian matrix for f(x,y)=x2y at (x,y)=(1,3).

∇2f=[3220]
∇2f=[3330]
∇2f=[6220]
∇2f=[6330]

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4. Let f(x,y)=−3×2−6xy−6y2. The point (0,0)is a

saddle point
maxima
minima

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6. For which numbers b is the matrix A=[1bb9] positive definite?

−3<b<3
b=3
b=−3
−3≤b≤3

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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. Consider the following optimization problem:

4×3+21×2+10x−17=0
12×2+42x+10=0
12×2+42x+10>0
12×2+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 minx f(x) can also be written as maxx f(x).

True
False

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10. Gradient descent algorithm converges to the local minimum.

True
False

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