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 .
Chapter 2, Problem 7T
(a)
To determine
The value of f(0) for the provided graph of y=f(x) as shown below.
(b)
To determine
The value of f(−4) for the provided graph of y=f(x) as shown below.
(c)
To determine
The values of x for which f(x)=2 for the provided graph of y=f(x) as shown below.
(d)
To determine
The intervals on which function f is increasing for the provided graph of y=f(x) as shown below
(e)
To determine
The intervals over which the function f is decreasing for the provided graph of y=f(x) as shown below.
(f)
To determine
The location and value of any relative minima for the provided graph of y=f(x) as shown below:
(g)
To determine
The location and value of any relative maxima for the provided graph of y=f(x) as shown below:
(h)
To determine
The domain of f for the provided graph of y=f(x) as shown below.
(i)
To determine
The range of f for the provided graph of y=f(x) as shown below.
(j)
To determine
Whether the function f is an even, odd or neither for the provided graph of y=f(x) as shown below.
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY