Differentiation and Integration Quiz

Question 1 of 9

1

Fill the blank space to complete the text.

Find an expression for the gradient of the function \[f(x) = 4x\] by differentiating from first principles.
Answer:

Explanation

Question 2 of 9

1

Which of the following is the derivative of the following equation:
\(y= 6x^2 + ^3 \sqrt{4x^2}\)

Select one of the following:

\[\frac{dy}{dx}=12x + \frac{8}{3x^3}\]
\[\frac{dy}{dx}=12x + \frac{8x^3}{3}\]
\[\frac{dy}{dx}=12x + \frac{8}{3}\]

Explanation

Question 3 of 9

1

If \(x\) represents displacement and \(t\) represents time, then which of the following represents acceleration?

Select one of the following:

\( x'(t) \)
\(\frac{dx}{dt}\)
\(x''\)

Explanation

Question 4 of 9

1

The second order derivative is zero at a local maximum.

Select one of the following:

True
False

Explanation

Question 5 of 9

1

The derivative of the function \[f(x) = 4x^2 + 5x^3 + 16\] is given by...

Select one of the following:

\(f'(x) = 8x + 15x^2\)
\(f'(x) = 12x^3 + 15x^4\)
\(f'(x) = 8x + 15x^2 +16\)

Explanation

Question 6 of 9

1

The graph of the derivative of this curve would have which shape?

Select one of the following:

Explanation

Question 7 of 9

1

Fill the blank space to complete the text.

Differentiate the following function:\[f(x) = \frac{3x^2+18x+8}{3x+2}\].
\(f'(x)\) =

Explanation

Question 8 of 9

1

To wrap up our learning series on Differentiation and Integration, we present this quiz to test your knowledge. Get a handle on how much you know by tacking these calculus questions to the best of your ability. Good luck!

Differentiation and Integration Quiz

Question 1 of 9

Fill the blank space to complete the text.

Find an expression for the gradient of the function \[f(x) = 4x\] by differentiating from first principles.
Answer:

Explanation

Question 2 of 9

Which of the following is the derivative of the following equation:
\(y= 6x^2 + ^3 \sqrt{4x^2}\)

Select one of the following:

Explanation

Question 3 of 9

If \(x\) represents displacement and \(t\) represents time, then which of the following represents acceleration?

Select one of the following:

Explanation

Question 4 of 9

The second order derivative is zero at a local maximum.

Select one of the following:

Explanation

Question 5 of 9

The derivative of the function \[f(x) = 4x^2 + 5x^3 + 16\] is given by...

Select one of the following:

Explanation

Question 6 of 9

The graph of the derivative of this curve would have which shape?

Select one of the following:

Explanation

Question 7 of 9

Fill the blank space to complete the text.

Differentiate the following function:\[f(x) = \frac{3x^2+18x+8}{3x+2}\].
\(f'(x)\) =

Explanation

Question 8 of 9

Fill the blank space to complete the text.

What is the gradient of the normal to the curve \[y= x^4 + 3x^2\] at the point \((1, 4)\)?
The gradient is .

Explanation

Question 9 of 9

Fill the blank space to complete the text.

Evaluate the following integral:
\[\int ^5_3 6x^2dx\]
Answer:

Explanation

	Created by Niamh Ryan over 7 years ago

To wrap up our learning series on Differentiation and Integration, we present this quiz to test your knowledge. Get a handle on how much you know by tacking these calculus questions to the best of your ability. Good luck!

Differentiation and Integration Quiz

Question 1 of 9

Fill the blank space to complete the text.

Find an expression for the gradient of the function \[f(x) = 4x\] by differentiating from first principles. Answer:

Explanation

Question 2 of 9

Which of the following is the derivative of the following equation: \(y= 6x^2 + ^3 \sqrt{4x^2}\)

Select one of the following:

Explanation

Question 3 of 9

If \(x\) represents displacement and \(t\) represents time, then which of the following represents acceleration?

Select one of the following:

Explanation

Question 4 of 9

The second order derivative is zero at a local maximum.

Select one of the following:

Explanation

Question 5 of 9

The derivative of the function \[f(x) = 4x^2 + 5x^3 + 16\] is given by...

Select one of the following:

Explanation

Question 6 of 9

The graph of the derivative of this curve would have which shape?

Select one of the following:

Explanation

Question 7 of 9

Fill the blank space to complete the text.

Differentiate the following function:\[f(x) = \frac{3x^2+18x+8}{3x+2}\]. \(f'(x)\) =

Explanation

Question 8 of 9

Fill the blank space to complete the text.

What is the gradient of the normal to the curve \[y= x^4 + 3x^2\] at the point \((1, 4)\)? The gradient is .

Explanation

Question 9 of 9

Fill the blank space to complete the text.

Evaluate the following integral: \[\int ^5_3 6x^2dx\] Answer:

Explanation

Find an expression for the gradient of the function \[f(x) = 4x\] by differentiating from first principles.
Answer:

Which of the following is the derivative of the following equation:
\(y= 6x^2 + ^3 \sqrt{4x^2}\)

Differentiate the following function:\[f(x) = \frac{3x^2+18x+8}{3x+2}\].
\(f'(x)\) =

What is the gradient of the normal to the curve \[y= x^4 + 3x^2\] at the point \((1, 4)\)?
The gradient is .

Evaluate the following integral:
\[\int ^5_3 6x^2dx\]
Answer: