Approximate the local maximum values and local minimum values of f ( x ) = x 2 − 5 x + 1 on [ − 4 , 4 ] . Determine where the function is increasing and where it is decreasing.
Approximate the local maximum values and local minimum values of f ( x ) = x 2 − 5 x + 1 on [ − 4 , 4 ] . Determine where the function is increasing and where it is decreasing.
Solution Summary: The author explains how to calculate the local maximum and local minimums of f (x) = x 3 5 + 1 on [ 4, 4].
Approximate the local maximum values and local minimum values of
on
. Determine where the function is increasing and where it is decreasing.
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
Expert Solution & Answer
To determine
To calculate: The local maximum and local minimums of on . Determine where the function is increasing and where it is decreasing.
Answer to Problem 13CR
Solution:
The local maxima occur at the point and the local minima occur at .
The graph of the function is increasing in the interval .
The function decreases at .
Explanation of Solution
Given:
The given function is on the interval .
Formula used:
We can find the values from the graph of the given equation.
Calculation:
From the graph, we can see that the local maxima occur at the point and the local minima occur at .
We can see from the graph that the function is increasing in the interval .
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