Question

match the graphs a - d of functions with graphs a - c of their derivatives. the graph of function a corresponds to the graph of derivative the graph of function b corresponds to the graph of derivative the graph of function c corresponds to the graph of derivative the graph of function d corresponds to the graph of derivative

Explanation:

Step1: Recall derivative - slope relationship

The derivative of a function at a point is the slope of the tangent line to the function at that point.

Step2: Analyze function a

Function a is a straight - line with a positive slope. Its derivative is a positive constant. Graph B is a horizontal line above the x - axis, representing a positive constant function, so the graph of function a corresponds to the graph of derivative B.

Step3: Analyze function b

Function b is a straight - line with a negative slope. Its derivative is a negative constant. Graph C is a horizontal line below the x - axis, representing a negative constant function, so the graph of function b corresponds to the graph of derivative C.

Step4: Analyze function c

Function c is a straight - line with a positive slope greater than that of function a. Its derivative is a positive constant greater than the derivative of function a. Since graph A is a horizontal line above the x - axis and higher than graph B, the graph of function c corresponds to the graph of derivative A.

Step5: Analyze function d

Function d is a horizontal line with slope 0. Its derivative is 0. There is no graph of derivative for function d among A - C.

Answer:

The graph of function a corresponds to the graph of derivative B.
The graph of function b corresponds to the graph of derivative C.
The graph of function c corresponds to the graph of derivative A.
The graph of function d has no corresponding graph of derivative among A - C.