What does it mean for f(x) if f'(x) has a maximum at x=1?

f(x) has a point of inflection at x=1

Derivatives, Power Rule, and rate of change questions

AP calculus rate of change, relationship between functions and their derivatives and the important points. Power rule, calculator, trig, exp #apcalculus #rateofchange #derivativespowerrule #derivativesusingacalculator #derivativesexponential #derivativestrigonometric

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Questions 31

Answers

1
Given f(x)=-6x², what is f"(2341)? (second derivative!)
-12
2341
-28092
-2341
2
d/dx (5e^x)
5xex-1
ex
5e-x
5ex
3
f(x)=1/x⁴, find f'(x)
-4/x5
-4/x3
4/x3
4/x5
4
What does it mean for f(x) if f'(x) has a maximum at x=1?
f(x) has a zero at x=1
f(x) has a point of inflection at x=1
f(x) has a minimum at x=1
f(x) has a maximum at x=1
5
f(x)=1/∛x, find f'(x)
1/√x
-1/3x-4/3
1/∜x
-1/3x-2/3
6
y=6cot(x)-5x³+1
6csc(x)cot(x)-15x2+1
-6csc(x)cot(x)-15x2
-6csc2(x)-15x2
6csc2(x)-15x2
7
What does it mean for f(x) if f'(x) changes from negative to positive at x=5, a zero of f'(x)?
f(x) has a minimum at x=5
f(x) has a maximum at x=5
Absolutely nothing
f(x) has a zero at x=5
8
y=-1/2cos(x)-2e^x
-1/2sin(x)-2xex-1
1/2sin(x)-2ex
1/2sin(x)-2ln(x)
-1/2sin(x)-2ex
9
d/dx -2tan(x)
2sec(x)tan(x)
-2sec(x)tan(x)
2sec2(x)
-2sec2(x)
10
y=x^-2, find y'
-2x-1
-2x-3
x-3
x-1
11
d/dx (x^1/4)
1/4x-1/4
1/4
1/4x-3/4
1/4x
12
What do you know about the value of a derivative, f', at a maximum of the function f?
The derivative has a point of inflection
The derivative has a maximum
The derivative has a minimum
The derivative has a zero
13
What is the second derivative of -2cos(x)?
-2sin(x)
-2cos(x)
2sin(x)
2cos(x)
14
If y=log(x), find y'
y'=(1/10)x
y'=10x * ln(10)
y'=1/x
y'=1/x * ln(10)
15
Given f'(3)=-2, is the function f(x) increasing, decreasing, or neither at x=3?
Decreasing
Neither
Increasing
16
f(x)=1-6x³+2x, find f'(x)
-18x2
18x2+2x
1-18x2
-18x2+2
17
Given f'(x)=-3/x²+5x+10, determine where f(x) has a maximum (Use your calculator!!!)
x=-1.8186
x=0
x=-0.6722
x=-1.06266
18
y=√x, find y'
1/(2x1/2)
1/2x1/2
2x-1/2
1/x
19
d/dx (1/x^7/2)
1/x9/2
1/x5/2
7/2x-5/2
-7/2x-9/2
20
d/dx (x)
x
0
1
1/x
21
y=-2sin(x), find y'
-2cos(x)
2sin(x)
2cos(x)
-2sin(x)
22
Given f(1)=5 and f(3)=11, approximate f'(2)
6
2
3
0
23
y=x⁵, find the SECOND derivative
y"=5x4
y"=20x4
y"=x3
y"=20x3
24
d/dx (ln x)
e-x
1/x
ex
ln x
25
d/dx -5csc(x)
5csc2x
-5csc(x)cot(x)
5csc(x)cot(x)
-5csc2x
26
Use your calculator to find f'(2) if f(x)=3x⁵-5x²+2
220.00012
0.71638849
DNE
78
27
y=4x³, find y'
12x3
3x2
4x2
12x2
28
d/dx sec(x)
sec(x)tan(x)
sec2x
1/cos(x)
tan2(x)
29
d/dx (5²)
25
0
5
10
30
d/dx (5x+326)
5+326/x
5
5x
331
31
f(x)=cos(x), find f'(x)
sin(x)
-cos(x)
-sin(x)
cos(x)

Derivatives, Power Rule, and rate of change questions Flashcards | StudBud

Derivatives, Power Rule, and rate of change questions

31 termsStudBud Administration56 plays

Flashcards31 cardsFPractice quizPHost liveL

Questions 31

Answers

1
Given f(x)=-6x², what is f"(2341)? (second derivative!)
-12
2341
-28092
-2341
2
d/dx (5e^x)
5xex-1
ex
5e-x
5ex
3
f(x)=1/x⁴, find f'(x)
-4/x5
-4/x3
4/x3
4/x5
4
What does it mean for f(x) if f'(x) has a maximum at x=1?
f(x) has a zero at x=1
f(x) has a point of inflection at x=1
f(x) has a minimum at x=1
f(x) has a maximum at x=1
5
f(x)=1/∛x, find f'(x)
1/√x
-1/3x-4/3
1/∜x
-1/3x-2/3
6
y=6cot(x)-5x³+1
6csc(x)cot(x)-15x2+1
-6csc(x)cot(x)-15x2
-6csc2(x)-15x2
6csc2(x)-15x2
7
What does it mean for f(x) if f'(x) changes from negative to positive at x=5, a zero of f'(x)?
f(x) has a minimum at x=5
f(x) has a maximum at x=5
Absolutely nothing
f(x) has a zero at x=5
8
y=-1/2cos(x)-2e^x
-1/2sin(x)-2xex-1
1/2sin(x)-2ex
1/2sin(x)-2ln(x)
-1/2sin(x)-2ex
9
d/dx -2tan(x)
2sec(x)tan(x)
-2sec(x)tan(x)
2sec2(x)
-2sec2(x)
10
y=x^-2, find y'
-2x-1
-2x-3
x-3
x-1
11
d/dx (x^1/4)
1/4x-1/4
1/4
1/4x-3/4
1/4x
12
What do you know about the value of a derivative, f', at a maximum of the function f?
The derivative has a point of inflection
The derivative has a maximum
The derivative has a minimum
The derivative has a zero
13
What is the second derivative of -2cos(x)?
-2sin(x)
-2cos(x)
2sin(x)
2cos(x)
14
If y=log(x), find y'
y'=(1/10)x
y'=10x * ln(10)
y'=1/x
y'=1/x * ln(10)
15
Given f'(3)=-2, is the function f(x) increasing, decreasing, or neither at x=3?
Decreasing
Neither
Increasing
16
f(x)=1-6x³+2x, find f'(x)
-18x2
18x2+2x
1-18x2
-18x2+2
17
Given f'(x)=-3/x²+5x+10, determine where f(x) has a maximum (Use your calculator!!!)
x=-1.8186
x=0
x=-0.6722
x=-1.06266
18
y=√x, find y'
1/(2x1/2)
1/2x1/2
2x-1/2
1/x
19
d/dx (1/x^7/2)
1/x9/2
1/x5/2
7/2x-5/2
-7/2x-9/2
20
d/dx (x)
x
0
1
1/x
21
y=-2sin(x), find y'
-2cos(x)
2sin(x)
2cos(x)
-2sin(x)
22
Given f(1)=5 and f(3)=11, approximate f'(2)
6
2
3
0
23
y=x⁵, find the SECOND derivative
y"=5x4
y"=20x4
y"=x3
y"=20x3
24
d/dx (ln x)
e-x
1/x
ex
ln x
25
d/dx -5csc(x)
5csc2x
-5csc(x)cot(x)
5csc(x)cot(x)
-5csc2x
26
Use your calculator to find f'(2) if f(x)=3x⁵-5x²+2
220.00012
0.71638849
DNE
78
27
y=4x³, find y'
12x3
3x2
4x2
12x2
28
d/dx sec(x)
sec(x)tan(x)
sec2x
1/cos(x)
tan2(x)
29
d/dx (5²)
25
0
5
10
30
d/dx (5x+326)
5+326/x
5
5x
331
31
f(x)=cos(x), find f'(x)
sin(x)
-cos(x)
-sin(x)
cos(x)