Calculus Concepts for Machine Learning Quiz

1. What is the derivative of f(x) = 3x² + 2x with respect to x?

6x + 2

3x + 2

6x² + 2x

X² + x

2. Momentum in gradient descent helps by which mechanism?

Accumulating gradient direction to accelerate convergence

Reducing the learning rate

Computing the Hessian matrix

Normalizing input features

3. If y = (3x + 1)⁵, what is dy/dx using the chain rule?

15(3x + 1)⁴

5(3x + 1)⁴

15x⁴

3(3x + 1)⁴

4. In gradient descent, what role does the learning rate play?

Controls step size in parameter updates

Determines the loss function

Measures model accuracy

Defines the activation function

5. What is a critical point of a function?

Where the derivative equals zero or is undefined

Where the function is continuous

Where the function is positive

Where the second derivative is positive

6. The partial derivative ∂f/∂x measures how f changes with respect to which variable?

X only, holding other variables constant

All variables simultaneously

Y only

The product of all variables

7. In optimization, a convex function has which property?

Any local minimum is also a global minimum

Multiple local minima exist

No critical points exist

The derivative is always positive

8. If f(x) = e^(2x), what is f'(x)?

2e^(2x)

E^(2x)

E^x

2e^x

9. Stochastic gradient descent uses which of the following to update parameters?

Gradient computed on a single or small batch of samples

Entire dataset gradient

Random weights

Fixed learning rate

10. In machine learning, the gradient of a loss function points in which direction?

Direction of steepest ascent

Direction of steepest descent

Direction of zero slope

Random direction

11. What is the derivative of f(x) = ln(x)?

1/x

X

E^x

1

12. What does the Hessian matrix contain?

Second-order partial derivatives

First-order partial derivatives

Eigenvalues of the covariance matrix

Singular values

13. What is the gradient vector in multivariable calculus?

Vector of all partial derivatives

Sum of all partial derivatives

Product of partial derivatives

Ratio of partial derivatives

14. In backpropagation, the chain rule is applied to compute gradients with respect to which?

Network weights and biases

Activation functions only

Input data

Batch size

15. What is the second derivative test used for in optimization?

Determining if critical points are maxima or minima

Computing the gradient

Finding inflection points

Solving differential equations

16. What does the chain rule allow you to compute?

Derivative of a composition of functions

Integral of polynomials

Sum of infinite series

Determinant of matrices

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DataX Calculus Concepts for Machine Learning Quiz