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Practice: Basic Derivatives Flashcards | StudBud
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Practice: Basic Derivatives
Practice: Basic Derivatives
12 terms
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#calculus #math #derivatives
Flashcards
12 cards
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Questions
12
Answers
1
What does it mean for a function to have a horizontal tangent at x?
It is undefined at x
It has a slope of 1
It is not differentiable
It has a slope of zero
2
Find derivative and simplify: f(x) = (x
2
)/(2x)
f '(x) = (-2x2)/(2x)2
f '(x) = (4x2+2x2)/(2x)2
f '(x) = (2x)2/(2x)2 = 1
f '(x) = (2x2)/(2x)2
3
Given f(x) = x
4
+ x
3
- x + 1, what is f '(1) ?
2
7
6
8
4
What does a derivative at a specific point tell you?
The rate of change at that point
The average rate of change
The slope of the whole line
The maximum or minimum of the function
5
Find the derivative of f(x) = 4x
1/2
+ 2
f '(x) = 8x-1/2
f '(x) = 2x1/2
f '(x) = 8x-1/2 + 2
f '(x) = 2x-1/2
6
Let f (x) = 6x
1/2
. What is the slope of the tangent line at x = 4?
6
3/2
3
3/4
7
What is the derivative of 7x
4
+ 3x
2
- 2x - 5?
28x4 + 6x2 - 2
28x4 + 6x2
28x4 + 6x2 - 2 - 5
28x3 + 6x - 2
8
Differentiate y = 3 sin x - 4 cos x
-3 cos x + 4 sin x
3 cos x + 4 cos x
3 cos x - 4 sin x
3 cos x + 4 sin x
9
Determine the x-value(s), if any, at which f (x) = x
3
+ 6x - 2 has a horizontal tangent.
x = 2
The graph has no horizontal tangents
x = -2
x = 3
10
What is the derivative of tan(x)?
1/(cos x)
1/(cos x2)
1/(cos x)2
1/(cos 2x)
11
Let f(x) = -2x
3
+ x
2
- 4x. What is the slope of the tangent line at x = 2 ?
24
-16
-24
16
12
Find the derivative of f(x) = 7x
-1
f ' (x) = -7x-2
f ' (x) = -7x
f ' (x) = -7x-1
f ' (x) = 7x-2
