Math  /  Calculus

QuestionThe domain of the function hh graphed below is all real numbers, and all of its extreme values occur when 3<x<3-3<x<3. Use the graph to answer the following questions.
Identify all of the values of cc for which h(c)h(c) is a local maximum of hh. If there is more than one value, enter the values as a comma-separated list. If there are none, enter DNE. values: \square
Identify all of the values of cc for which h(c)h(c) is a local minimum of hh. If there is more than one value, enter the values as a comma-separated list. If there are none, enter DNE. values: \square

Studdy Solution

STEP 1

1. The function h(x) h(x) is continuous and defined for all real numbers.
2. All extreme values (local maxima and minima) occur within the interval 3<x<3-3 < x < 3.
3. We are given a graph to visually identify local maxima and minima.

STEP 2

1. Identify local maxima from the graph.
2. Identify local minima from the graph.

STEP 3

Examine the graph to identify peaks within the interval 3<x<3-3 < x < 3.

STEP 4

From the graph description, there is a peak around x=1 x = 1 , indicating a local maximum.

STEP 5

Examine the graph to identify valleys within the interval 3<x<3-3 < x < 3.

STEP 6

From the graph description, there is a valley around x=1 x = -1 , indicating a local minimum. Additionally, there is another dip near x=0 x = 0 , indicating another local minimum.
Identified values for local maxima: 1 \boxed{1}
Identified values for local minima: 1,0 \boxed{-1, 0}

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