Final answer:
The function tells you the relationship between the variables, the derivative tells you the slope, and the second derivative tells you the concavity.
Step-by-step explanation:
The function, derivative, and second derivative can provide information about the graph of a function. Here's what each can inform you on:
Function:
The function itself represents the relationship between the independent variable (usually denoted as 'x') and the dependent variable (usually denoted as 'y'). The graph of the function shows how the values of 'y' change with respect to 'x'.
Derivative:
The derivative measures the rate of change of the function at a specific point. It provides information about the slope of the graph at that point. If the derivative is positive, the function is increasing; if it's negative, the function is decreasing.
Second Derivative:
The second derivative describes how the rate of change (slope) of the function itself is changing. It can help identify whether the graph is concave up (opening upwards) or concave down (opening downwards).