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.
3) Use the following system of linear inequalities graphed below to answer the questions.
a) Use the graph to write the symbolic form of the system
of linear inequalities.
b) Is (-4,2) a solution to the system? Explain.
5
-7
-5
-3
-2
0
2
3
4
$
6
-2
-6
-7
) Graph the feasible region subject to the following constraints.
x + y ≤ 6
y ≤ 2x
x ≥ 0, y ≥ 0
P
+
x
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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