Use the graph of f to determine each of the following. Where applicable, use interval notation. a. the domain of f b. the range of f c. the x -intercepts d. they y -intercept e. intervals on which f is increasing f. intervals on which f is decreasing g. values of x for which f ( x ) ≤ 0 h. the numbers at which f has a relative maximum i. the relative maxima of f j. f ( − 2 ) k. the values of x for which f ( x ) − 0 i. Is f even, odd, or neither?
Use the graph of f to determine each of the following. Where applicable, use interval notation. a. the domain of f b. the range of f c. the x -intercepts d. they y -intercept e. intervals on which f is increasing f. intervals on which f is decreasing g. values of x for which f ( x ) ≤ 0 h. the numbers at which f has a relative maximum i. the relative maxima of f j. f ( − 2 ) k. the values of x for which f ( x ) − 0 i. Is f even, odd, or neither?
Solution Summary: The author explains the domain of f whose graph is: Solution: x -values are the input values to the function, the graph of which is plotted.
Use the graph of f to determine each of the following. Where applicable, use interval notation.
a. the domain of f
b. the range of f
c. the x -intercepts
d. they y -intercept
e. intervals on which f is increasing
f. intervals on which f is decreasing
g. values of x for which
f
(
x
)
≤
0
h. the numbers at which f has a relative maximum
i. the relative maxima of f
j.
f
(
−
2
)
k. the values of x for which
f
(
x
)
−
0
i. Is f even, odd, or neither?
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 .
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Chapter 1 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Precalculus (6th Edition)
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