Math Problem Statement

List the intervals where f is decreasing

List the intervals where f is decreasing

Solution

To determine where the function f(x)f(x) is decreasing, we need to observe the intervals on the graph where the slope of the curve is negative, meaning the function is sloping downwards as we move from left to right.

From the graph you provided:

  • The function is decreasing from approximately x=10x = -10 to x=2x = -2 (left side of the curve as it moves downward).
  • The function starts decreasing again from x=4x = 4 to x=10x = 10 (right side of the curve after it reaches its peak at x=4x = 4).

So, the intervals where f(x)f(x) is decreasing are: (10,2)(4,10)(-10, -2) \cup (4, 10)

Would you like further details or have any questions about this?

Here are 5 related questions for practice:

  1. What are the intervals where the function is increasing?
  2. Can you identify the relative minimum and maximum points?
  3. What is the value of f(x)f(x) at x=0x = 0?
  4. How would you estimate the average rate of change of the function between x=10x = -10 and x=2x = -2?
  5. What kind of symmetry does this function exhibit, if any?

Tip: To determine if a function is increasing or decreasing, always check the sign of the derivative or visually inspect where the graph slopes up or down!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Calculus
Graphing
Rates of Change

Formulas

Interval notation for increasing/decreasing functions
Derivative of f(x) to find intervals of increasing or decreasing

Theorems

First Derivative Test

Suitable Grade Level

Grades 10-12