Differentiation and Integration Quiz

Question 1

Question

Find an expression for the gradient of the function

$f(x) = 4x$ by differentiating from first principles. Answer: [blank_start]4[blank_end]

Answer

Question 2

Question

Which of the following is the derivative of the following equation:

$y= 6x^2 + ^3 \sqrt{4x^2}$

Answer

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

Question 3

Question

$x$ represents displacement and

$t$ represents time, then which of the following represents acceleration?

Answer

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

Question 4

Question

The second order derivative is zero at a local maximum.

Answer

True
False

Question 5

Question

The derivative of the function

$f(x) = 4x^2 + 5x^3 + 16$ is given by...

Answer

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

Question 6

Question

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

Image:

Desmos Graph (2) (binary/octet-stream)

Answer

Image:
Quadratic Graph 2 (binary/octet-stream)
Image:
Geenric Linear Graph (binary/octet-stream)
Image:
Geenric Constant Graph (binary/octet-stream)

Question 7

Question

Differentiate the following function:

$f(x) = \frac{3x^2+18x+8}{3x+2}$ .

$f'(x)$ = [blank_start]1[blank_end]

Answer

Question 8

Question

What is the gradient of the normal to the curve

$y= x^4 + 3x^2$ at the point

$(1, 4)$ ? The gradient is [blank_start]-1/10[blank_end].

Answer

-1/10

Question 9

Question

Evaluate the following integral:

$\int ^5_3 6x^2dx$ Answer: [blank_start]96[blank_end]

Answer

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Differentiation and Integration Quiz

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Resource summary

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

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	Created by Niamh Ryan almost 8 years ago