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 .
An engineer is designing a pipeline which is supposed to connect two points P and S. The engineer decides
to do it in three sections. The first section runs from point P to point Q, and costs $48 per mile to lay, the
second section runs from point Q to point R and costs $54 per mile, the third runs from point R to point S
and costs $44 per mile. Looking at the diagram below, you see that if you know the lengths marked x and y,
then you know the positions of Q and R. Find the values of x and y which minimize the cost of the pipeline.
Please show your answers to 4 decimal places.
2 Miles
x =
1 Mile
R
10 miles
miles
y =
miles
An open-top rectangular box is being constructed to hold a volume of 150 in³. The base of the box is made
from a material costing 7 cents/in². The front of the box must be decorated, and will cost 11 cents/in².
The remainder of the sides will cost 3 cents/in².
Find the dimensions that will minimize the cost of constructing this box. Please show your answers to at
least 4 decimal places.
Front width:
Depth:
in.
in.
Height:
in.
Find and classify the critical points of z = (x² – 8x) (y² – 6y).
Local maximums:
Local minimums:
Saddle points:
-
For each classification, enter a list of ordered pairs (x, y) where the max/min/saddle occurs. Enter DNE if
there are no points for a classification.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.