The correct statement from the given options for the condition when the graph of y = sin x has a relative minimum at x . (a). y = csc x is undefined. (b). y = sec x is undefined. (c). The graph of y = sec x has a relative maximum at x . (d). The graph of y = csc x has a relative minimum at x . (e). The graph of y = sec x has a vertical asymptote. (f). The graph of y = csc x has a vertical asymptote. (g). The graph of y = csc x has a relative maximum at x . (h). The graph of y = sec x has a relative minimum at x .
The correct statement from the given options for the condition when the graph of y = sin x has a relative minimum at x . (a). y = csc x is undefined. (b). y = sec x is undefined. (c). The graph of y = sec x has a relative maximum at x . (d). The graph of y = csc x has a relative minimum at x . (e). The graph of y = sec x has a vertical asymptote. (f). The graph of y = csc x has a vertical asymptote. (g). The graph of y = csc x has a relative maximum at x . (h). The graph of y = sec x has a relative minimum at x .
Solution Summary: The author explains that the graph of y=mathrmcscx suggests that at the values where the function
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 4.6, Problem 14PE
To determine
The correct statement from the given options for the condition when the graph of y=sinx has a relative minimum at x .
(a). y=cscx is undefined.
(b). y=secx is undefined.
(c). The graph of y=secx has a relative maximum at x .
(d). The graph of y=cscx has a relative minimum at x .
(e). The graph of y=secx has a vertical asymptote.
(f). The graph of y=cscx has a vertical asymptote.
(g). The graph of y=cscx has a relative maximum at x .
(h). The graph of y=secx has a relative minimum at x .
The number of fish swimming upstream to spawn is approximated by the function given below, where x represents the temperature of the water in degrees Celsius. Find the water
temperature that produces the maximum number of fish swimming upstream.
F(x) = x3 + 3x² + 360x + 5017, 5≤x≤18
A campground owner has 500 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the sketch.)
Let x represent the width of the field.
(a) Write an expression for the length of the field as a function of x.
(b) Find the area of the field (area = length x width) as a function of x.
(c) Find the value of x leading to the maximum area.
(d) Find the maximum area.
x
River
A rectangular tank with a square base, an open top, and a volume of 1372 ft³ is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface
area.
The dimensions of the tank with minimum surface area are
(Simplify your answer. Use a comma to separate answers.)
ft.
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