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Questions and Answers
What is a relative maximum value of a function?
What is a relative maximum value of a function?
- The value at which the function has a zero derivative
- The value at which the function does not exist
- The value at which the function reaches its highest point in the given interval (correct)
- The value at which the function reaches its lowest point in the given interval
What is a relative minimum value of a function?
What is a relative minimum value of a function?
- The value at which the function reaches its highest point in the given interval
- The value at which the function has a zero derivative
- The value at which the function reaches its lowest point in the given interval (correct)
- The value at which the function does not exist
When is a number considered to be a relative extremum value of a function?
When is a number considered to be a relative extremum value of a function?
- When the function has a zero derivative at that number
- When the function has a non-existent derivative at that number
- When the function reaches its maximum or minimum value at that number (correct)
- When the function does not exist at that number
According to Theorem 4.1, if 𝑓𝑓(𝑐𝑐) is a relative extremum value, what is the value of 𝑓𝑓’(𝑐𝑐)?
According to Theorem 4.1, if 𝑓𝑓(𝑐𝑐) is a relative extremum value, what is the value of 𝑓𝑓’(𝑐𝑐)?
What is a critical value of a function?
What is a critical value of a function?
In Example: Find the critical values of 𝑓𝑓(𝑥𝑥) = $𝑥^3 - 3𝑥^2 - 9𝑥 + 1$, what are the critical values?
In Example: Find the critical values of 𝑓𝑓(𝑥𝑥) = $𝑥^3 - 3𝑥^2 - 9𝑥 + 1$, what are the critical values?
What is the first derivative of the function 𝑓(𝑥) = $3𝑥^2 - 6𝑥 - 9$?
What is the first derivative of the function 𝑓(𝑥) = $3𝑥^2 - 6𝑥 - 9$?
Which of the following is a critical value of the function 𝑓(𝑥) = $3𝑥^2 - 6𝑥 - 9$?
Which of the following is a critical value of the function 𝑓(𝑥) = $3𝑥^2 - 6𝑥 - 9$?
What is the derivative of the absolute value function 𝑔(𝑥) = |𝑥|?
What is the derivative of the absolute value function 𝑔(𝑥) = |𝑥|?
For what value of 𝑐 is the absolute value function 𝑔(𝑥) = |𝑥| not differentiable?
For what value of 𝑐 is the absolute value function 𝑔(𝑥) = |𝑥| not differentiable?
According to Theorem 4.2, when does a function have an absolute maximum and an absolute minimum?
According to Theorem 4.2, when does a function have an absolute maximum and an absolute minimum?
What type of function is 𝑓(𝑥) = $3𝑥^2 - 6𝑥 - 9$ on the interval [a, b] if 𝑓'(𝑥) ≥ 0 for all 𝑥 in (a, b)?
What type of function is 𝑓(𝑥) = $3𝑥^2 - 6𝑥 - 9$ on the interval [a, b] if 𝑓'(𝑥) ≥ 0 for all 𝑥 in (a, b)?
If 𝑓′(𝑥) ≤ 0 for all 𝑥 in (a, b), what type of function is 𝑓(𝑥) = $3𝑥^2 - 6𝑥 - 9$ on the interval [a, b]?
If 𝑓′(𝑥) ≤ 0 for all 𝑥 in (a, b), what type of function is 𝑓(𝑥) = $3𝑥^2 - 6𝑥 - 9$ on the interval [a, b]?
In Theorem 4.4, if 𝑓′(𝑥) ≥ 0 as 𝑥 approaches 𝑐 from the left and 𝑓′(𝑥) ≤ 0 as 𝑥 approaches 𝑐 from the right, what can be concluded about 𝑓(𝑐)?
In Theorem 4.4, if 𝑓′(𝑥) ≥ 0 as 𝑥 approaches 𝑐 from the left and 𝑓′(𝑥) ≤ 0 as 𝑥 approaches 𝑐 from the right, what can be concluded about 𝑓(𝑐)?
What does Theorem 4.3 state about the behavior of a function when its first derivative is always non-negative on an interval?
What does Theorem 4.3 state about the behavior of a function when its first derivative is always non-negative on an interval?
When does a number qualify as an absolute extremum value on an interval?
When does a number qualify as an absolute extremum value on an interval?
What type of function is defined as strictly increasing on an interval if its values consistently increase and never decrease?
What type of function is defined as strictly increasing on an interval if its values consistently increase and never decrease?
If a function’s values consistently decrease as the input values increase, what type of function is it described as?
If a function’s values consistently decrease as the input values increase, what type of function is it described as?
What is the domain of the function $f(x) = an(x)$?
What is the domain of the function $f(x) = an(x)$?
What is the range of the function $f(x) = \sqrt{x}$?
What is the range of the function $f(x) = \sqrt{x}$?
Which function is defined on the interval $(0, +\infty)$?
Which function is defined on the interval $(0, +\infty)$?
What is the domain of the function $f(x) = \frac{1}{x}$?
What is the domain of the function $f(x) = \frac{1}{x}$?
What is the range of the function $f(x) = \ln(x)$?
What is the range of the function $f(x) = \ln(x)$?
Which function has a range of $(-\infty, -1] \cup [1, +\infty)$?
Which function has a range of $(-\infty, -1] \cup [1, +\infty)$?
What is the domain of the function $f(x) = \sqrt{x}$?
What is the domain of the function $f(x) = \sqrt{x}$?
Which function has a range of $[0, +\infty)$?
Which function has a range of $[0, +\infty)$?
What is the domain of the function $f(x) = 2^x$?
What is the domain of the function $f(x) = 2^x$?
Which function is defined on the interval $(-\infty,-1] \cup [1,+\infty)$?
Which function is defined on the interval $(-\infty,-1] \cup [1,+\infty)$?
What is the domain of the function resulting from the addition (𝐹𝐹 + 𝐺𝐺)(𝑥𝑥)?
What is the domain of the function resulting from the addition (𝐹𝐹 + 𝐺𝐺)(𝑥𝑥)?
What is the domain of the function resulting from the subtraction (𝐹𝐹– 𝐺𝐺)(𝑥𝑥)?
What is the domain of the function resulting from the subtraction (𝐹𝐹– 𝐺𝐺)(𝑥𝑥)?
What is the domain of the function resulting from the composition (ℎ𝑥1 ∘ ℎ𝑥2)(𝑥)?
What is the domain of the function resulting from the composition (ℎ𝑥1 ∘ ℎ𝑥2)(𝑥)?
What is the domain of the function resulting from the division (� �)(𝑥)?
What is the domain of the function resulting from the division (� �)(𝑥)?
What is the domain of the function 𝑅𝑅 resulting from the square root operation?
What is the domain of the function 𝑅𝑅 resulting from the square root operation?
What is the domain of the function 𝑃𝑃 resulting from √� �?
What is the domain of the function 𝑃𝑃 resulting from √� �?
What is the domain of the function 𝐻𝐻 resulting from (�1 � �2 )(�)?
What is the domain of the function 𝐻𝐻 resulting from (�1 � �2 )(�)?
What is the domain of the function 𝑄𝑄 resulting from csc�√� �2 − � − 2�?
What is the domain of the function 𝑄𝑄 resulting from csc�√� �2 − � − 2�?
What is the domain of 𝐹� � resulting from �1 � �2 ?
What is the domain of 𝐹� � resulting from �1 � �2 ?
What is the domain of 𝑃� � resulting from √� �2 − � − 2�?
What is the domain of 𝑃� � resulting from √� �2 − � − 2�?
What is the domain of �(�1 � �2 )(�)?
What is the domain of �(�1 � �2 )(�)?
What is the domain of � resulting from csc�√� �2 − � − 2�?
What is the domain of � resulting from csc�√� �2 − � − 2�?
