MAT 122 Quiz: MAT 122 SBU Quiz 4 Solution

• School: Stony Brook University
• Department: Mathematics
• Course: MAT 122
• Professor: All

Document Summary

Question 1: the graph of some function f (x) is shown below. The function is increasing on the intervals ( 1, 0) and (2, ). The graph has horizontal tangent lines when x = 1, x = 0, and x = 2. (c) on the axes below, sketch a graph of the derivative function f 0(x). Explain why your graph agrees with your answers in parts (a) and (b). The value of f 0(x) is positive on the same intervals that f (x) is increasing, and negative on the same intervals the original function is decreasing. The derivative function has zeros (x-intercepts) at the same x-values that the original function has horizontal tangent lines. Question 2: consider the function g(x) = x3. The derivative of this function is g0(x) = 2 (we"ll learn in a later chapter how to nd this derivative). 3x2 line through the graph of g(x) at the point x = 0.