9731390
Description
Quiz by Niamh Ryan, updated more than 1 year ago
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Created by Niamh Ryan
almost 7 years ago
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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
-
4
Question 2
Question
Which of the following is the derivative of the following equation:
\(y= 6x^2 + ^3 \sqrt{4x^2}\)
Answer
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\[\frac{dy}{dx}=12x + \frac{8}{3x^3}\]
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\[\frac{dy}{dx}=12x + \frac{8x^3}{3}\]
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\[\frac{dy}{dx}=12x + \frac{8}{3}\]
Question 3
Question
If \(x\) represents displacement and \(t\) represents time, then which of the following represents acceleration?
Answer
-
\( x'(t) \)
-
\(\frac{dx}{dt}\)
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\(x''\)
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
-
\(f'(x) = 8x + 15x^2\)
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\(f'(x) = 12x^3 + 15x^4\)
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\(f'(x) = 8x + 15x^2 +16\)
Question 6
Question
The graph of the derivative of this curve would have which shape?
Answer
Question 7
Question
Differentiate the following function:\[f(x) = \frac{3x^2+18x+8}{3x+2}\].
\(f'(x)\) = [blank_start]1[blank_end]
Answer
-
1
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
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-1/10
Question 9
Question
Evaluate the following integral:
\[\int ^5_3 6x^2dx\]
Answer: [blank_start]96[blank_end]
Answer
-
96
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