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Basic Derivatives (All Questions) Flashcards | StudBud
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Basic Derivatives (All Questions)
Basic Derivatives (All Questions)
23 terms
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#calculus #math #derivatives
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Answers
1
What is the derivative of 3x
4
+ 5x?
7x3 + 5
12x + 5
12x3 + 5
12x4 + 5
2
What does a derivative at a specific point tell you?
The maximum or minimum of the function
The average rate of change
The rate of change at that point
The slope of the whole line
3
Find derivative and simplify: f(x) = (x
2
)/(2x)
f '(x) = (2x2)/(2x)2
f '(x) = (4x2+2x2)/(2x)2
f '(x) = (-2x2)/(2x)2
f '(x) = (2x)2/(2x)2 = 1
4
What is the derivative of 5x
6
+ 8x
2
+ 10?
30x5 + 16x
30x6 + 16x2
30x6 + 16x2 + 10
30x5 + 16x + 10
5
What is the derivative of the function f(x)= sin(x)+3x?
-sec(x) + 3
tan(x) + 3
-cos(x) + 3
cos(x) + 3
6
What is the derivative of the function F(x) = (x
2
+3x)
3
?
F '(x) = 3(x2+3x)(2x+3)
F '(x) = 3(2x+3)2
F '(x) = 3(x2+3x)2(2x+3)
F '(x) = (2x+3)2
7
Find the derivative of f(x) = x
4
+ 5x
f '(x) = 4x3
f '(x) = 4x2 + 5
f '(x) = 3x4 + 5x
f '(x) = 4x3 + 5
8
What is the derivative of y = 3x + x tan(x)?
3 + (x/cos2(x)) + tan(x)
3 + x tan(x)
3 + x sec(x) + tan(x)
3x + x tan(x)
9
Find the derivative of y = cos4x
4cos(4x)
-4cos(x)
-4sin(4x)
-4xsin(4x)
10
What does it mean for a function to have a horizontal tangent at x?
It is undefined at x
It has no slope at x
It is not differentiable
It has a slope of zero
11
Find the derivative and simplify: (4x
2
)/(2x
3
)
(16x4+24x4)/(2x3)2
(8x4)/(2x3)2
(8x)(2x3)+(6x2)(4x2)/(2x3)
-2x-2
12
If f(x) = ln e
2x
, what is f '(x)?
f '(x) = 1/e2x
f '(x) = 2/e2x
f '(x) = 2x
f '(x) = 2
13
Let f(x) = -2x
3
+ x
2
- 4x. What is the slope of the tangent line at x = 2 ?
-24
24
-16
16
14
Find the average rate of change of f(x) = x
2
+ 2x over the interval (1, 2)
4
5
6
7
15
What is the derivative of 7x
4
+ 3x
2
- 2x - 5?
28x4 + 6x2
28x4 + 6x2 - 2 - 5
28x4 + 6x2 - 2
28x3 + 6x - 2
16
Let f (x) = 6x
1/2
. What is the slope of the tangent line at x = 4?
3/2
3/4
6
3
17
What is the derivative of f(x) = (x
2
+1)(x
3
+3)?
x4-3x2+6x
5x2+3x+6
5x4+3x2+6x
5x4-3x2+6
18
Find the derivative of f(x) = 4x
1/2
+ 2
f '(x) = 8x-1/2 + 2
f '(x) = 2x-1/2
f '(x) = 2x1/2
f '(x) = 8x-1/2
19
Given f(x) = x
4
+ x
3
- x + 1, what is f '(1) ?
8
2
7
6
20
Find the derivative of y = (3x+4)
3
9(3x+4)2
9(3x+4)3
9(3x-4)2
3(3x+4)2+3
21
Find the derivative of f(x) = 7x
-1
f ' (x) = -7x-1
f ' (x) = -7x-2
f ' (x) = 7x-2
f ' (x) = -7x
22
Let f(x) = x
4
+ 3x + 6. What is the slope of the tangent line at x = 1?
13
7
4
10
23
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
