Quiz About Derivatives To Analyze Functions

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Questions: 10 | Attempts: 162 | Updated: Mar 18, 2023

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Quiz About Derivatives To Analyze Functions - Quiz

Derivatives as known to be used to describe the variation or rate of change between two points. Their rules vary depending on the nature of a function (whether you are dealing with a linear function or a power function). Do you think you are armed enough when it comes to derivative rules used to analyze functions? Take our quiz and see how good you are.

Questions and Answers

1.

Given the function, f(x), when f'x<0 over a given interval, then f(x) should be described as?
- A.
  
  Decreasing
- B.
  
  Increasing
- C.
  
  Being constant
- D.
  
  Concave down
Correct Answer
A. Decreasing

Explanation
If the derivative of a function, f'(x), is negative over a given interval, it means that the slope of the function is negative in that interval. This implies that as x increases, the function f(x) decreases. Therefore, f(x) should be described as "decreasing" over the given interval.

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2.

Given a function f(x), when f'(x) >0 over a given interval, then fx is described as ?
- A.
  
  Decreasing
- B.
  
  Increasing
- C.
  
  Stagnant
- D.
  
  Indefined
Correct Answer
B. Increasing

Explanation
When the derivative of a function f(x) is greater than 0 over a given interval, it means that the function is increasing over that interval. This is because a positive derivative indicates that the slope of the function is positive, which implies that the function is getting larger as x increases. Therefore, the correct answer is "Increasing".

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3.

Given a function g(x), f g"(x)=0 for a given value of x, then g(x) should have what at point x?
- A.
  
  A negative value
- B.
  
  A value of 1
- C.
  
  A value of 0
- D.
  
  An inflection point
Correct Answer
D. An inflection point

Explanation
If the second derivative of g(x), g''(x), is equal to 0 for a given value of x, it means that the graph of g(x) has a point of inflection at that x value. An inflection point is a point on a curve where the curve changes concavity, transitioning from being concave up to concave down, or vice versa. Therefore, the correct answer is "An inflection point."

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4.

Given a function g(x), when g'(x) =0 at a certain value of x, then g(x) has what at point x?
- A.
  
  A critical point
- B.
  
  A concave point
- C.
  
  A negative value
- D.
  
  A positive value
Correct Answer
A. A critical point

Explanation
When the derivative of a function, g'(x), is equal to zero at a certain value of x, it indicates that the function has a critical point at that specific point. A critical point is a point on the graph of the function where the slope of the tangent line is either zero or undefined. Therefore, the correct answer is "A critical point."

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5.

For a function f(x), f"(4)=0 indicates that x=4 is what?
- A.
  
  An infliction point.
- B.
  
  A negative point.
- C.
  
  A progressive point.
- D.
  
  A regressive point.
Correct Answer
A. An infliction point.

Explanation
The statement f"(4)=0 indicates that the second derivative of the function f(x) at x=4 is equal to zero. In calculus, when the second derivative is zero at a specific point, it suggests that the function has a point of inflection at that point. A point of inflection is a point on the graph where the concavity changes, transitioning from being concave up to concave down, or vice versa. Therefore, the correct answer is "An infliction point."

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6.

For a function g(x), g'(-2)=0 indicates that x=-2 is what?
- A.
  
  Parallel to b
- B.
  
  Parallel to C
- C.
  
  A critical point.
- D.
  
  Equal to 0
Correct Answer
C. A critical point.

Explanation
When g'(-2) = 0, it means that the derivative of the function g(x) at x = -2 is equal to zero. This indicates that x = -2 is a critical point of the function. A critical point is a point where the slope of the function is either zero or undefined. It can be a minimum, maximum, or an inflection point. Therefore, the correct answer is "A critical point."

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7.

For a function f(x), f'(-3)=5 indiactes that f(x) is doig what at x=-3?
- A.
  
  Stagnating
- B.
  
  Increasing
- C.
  
  Decreasing
- D.
  
  Disappearing
Correct Answer
B. Increasing

Explanation
The given information f'(-3)=5 indicates that the derivative of the function f(x) at x=-3 is positive. Since the derivative represents the rate of change of the function, a positive derivative means that the function is increasing at x=-3. Therefore, the correct answer is "Increasing."

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8.

For as function g(x); g"(3)=-8 indicates that g(x) is what at x=3?
- A.
  
  Decreasing
- B.
  
  Increasing
- C.
  
  Concave up
- D.
  
  Concave down
Correct Answer
D. Concave down

Explanation
The given information g"(3) = -8 indicates that the second derivative of the function g(x) at x=3 is negative. In calculus, the second derivative is used to determine the concavity of a function. If the second derivative is negative, it means that the function is concave down at that point. Therefore, the correct answer is concave down.

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9.

The slope of a function is described by what?
- A.
  
  Its first derivative
- B.
  
  Its second derivative
- C.
  
  Its last derivative
- D.
  
  Point y.
Correct Answer
A. Its first derivative

Explanation
The slope of a function is determined by its first derivative. The first derivative of a function represents the rate of change of the function at any given point. By calculating the first derivative, we can find the slope of the function at different points on its graph. Therefore, the correct answer is "Its first derivative."

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10.

The concavity of a function is described by what?
- A.
  
  Its first derivative
- B.
  
  Its second derivative
- C.
  
  The final result
- D.
  
  By the value of x
Correct Answer
B. Its second derivative

Explanation
The concavity of a function is described by its second derivative. The second derivative measures the rate of change of the slope of the function, indicating whether the function is concave up or concave down. A positive second derivative indicates concavity upwards, while a negative second derivative indicates concavity downwards. Therefore, the second derivative is the key factor in determining the concavity of a function.

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Quiz About Derivatives To Analyze Functions

Given the function, f(x), when f'x<0 over a given interval, then f(x) should be described as?

Given a function f(x), when f'(x) >0 over a given interval, then fx is described as ?

Given a function g(x), f g"(x)=0 for a given value of x, then g(x) should have what at point x?

Given a function g(x), when g'(x) =0 at a certain value of x, then g(x) has what at point x?

For a function f(x), f"(4)=0 indicates that x=4 is what?

For a function g(x), g'(-2)=0 indicates that x=-2 is what?

For a function f(x), f'(-3)=5 indiactes that f(x) is doig what at x=-3?

For as function g(x); g"(3)=-8 indicates that g(x) is what at x=3?

The slope of a function is described by what?

The concavity of a function is described by what?