1.
Rate of change with respect to a variable is termed...
Correct Answer
B. Differentiation
Explanation
Differentiation is the correct term for the rate of change with respect to a variable. It refers to the process of finding the derivative of a function, which represents the rate at which the function is changing at any given point. Differentiation is used in calculus to analyze the slope, velocity, and acceleration of functions, making it the appropriate choice for describing the rate of change.
2.
The instantaneous rate of change of a function with respect to one of its variables is the...
Correct Answer
C. Derivative
Explanation
The instantaneous rate of change of a function with respect to one of its variables is the derivative. The derivative measures how the function changes at a specific point, representing the slope of the tangent line to the function's graph at that point. It provides information about the rate at which the function is increasing or decreasing at that point.
3.
Which of these is not a rule of differentiation?
Correct Answer
D. Low rule
Explanation
The correct answer is "Low rule." However, there is no rule of differentiation called "Low rule." This could be a typographical error or a made-up rule. The other options, chain rule, power rule, and product rule, are well-known and widely used rules in differentiation.
4.
The reverse process of differentiation is...
Correct Answer
B. Integration
Explanation
The reverse process of differentiation is integration. Integration involves finding the antiderivative of a function, which essentially means finding the original function that would give the derivative of the given function. It is the opposite operation of differentiation, where we find the rate of change of a function. Integration allows us to find the total accumulation or area under a curve, and it is an important concept in calculus.
5.
The algebraic method of finding the derivative for a function at any point is...
Correct Answer
A. Differentiation
Explanation
Differentiation is the algebraic method of finding the derivative for a function at any point. It involves calculating the rate at which the function changes with respect to its independent variable. By finding the derivative, we can determine the slope of the tangent line to the function at a specific point, which provides valuable information about the behavior of the function. Therefore, Differentiation is the correct answer as it accurately describes the process of finding the derivative using algebraic methods.
6.
The slope of the tangent line to the function f at the point a is the...
Correct Answer
A. Derivative
Explanation
The slope of the tangent line to a function at a specific point is given by its derivative. The derivative represents the rate of change of the function at that point and provides information about how the function is behaving locally. Therefore, the correct answer is "Derivative".
7.
The derivative of a constant is...
Correct Answer
C. 0
Explanation
The derivative of a constant is 0 because a constant value does not change as x varies. Therefore, its rate of change is always 0.
8.
A group of functions with similar characteristics is called?
Correct Answer
B. Family of functions
Explanation
A group of functions with similar characteristics is called a family of functions because they share common features or behaviors. This term emphasizes the relationship between the functions and highlights their similarities, suggesting that they belong to the same group or category. It implies that these functions have certain common properties or patterns that distinguish them from other functions.
9.
The slope of the tangent line at a point on a graph is the...
Correct Answer
B. Derivative
Explanation
The slope of the tangent line at a point on a graph is the derivative. The derivative represents the rate of change of a function at a specific point. It gives us the slope of the tangent line, which is the line that touches the graph at that point and represents the instantaneous rate of change of the function at that point. Therefore, the correct answer is derivative.
10.
The amount by which a function is changing at one given point is the...
Correct Answer
D. Derivative
Explanation
The derivative of a function represents the rate at which the function is changing at a specific point. It measures the slope of the function at that point, indicating whether the function is increasing or decreasing and how quickly. Therefore, the correct answer is "Derivative."