The absolute maximum and minimum of a function on a given interval can be found by calculating the function's critical points and evaluating the function at these points and the interval endpoints, then comparing these values.
In order to find the absolute maximum and absolute minimum values of a function on a given interval, you must first find the critical points of the function within the interval. Critical points occur where the derivative of the function is equal to zero or is undefined. In this case, the derivative of f(t) = 9t + 9 cot(t/2) is f'(t) = 9 - (9/2) csc2(t/2). Set this to zero and solve for t to find the critical points. Additionally, the endpoints of the interval, π/4 and 7π/4, could be the absolute maximum or minimum, so these should be evaluated as well. Once you have found the values of the function at these points and the endpoints, compare them to determine the absolute maximum and minimum values.
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To find the absolute maximum and minimum values of a function, we find the critical points and endpoints. Evaluating the function at these points gives the maximum and minimum values.
To find the absolute maximum and absolute minimum values of a function on a given interval, we need to find the critical points and endpoints of the interval.
To find the critical points of f, we need to find where the derivative of f is equal to zero or undefined. The derivative of f(t) = 9t + 9cot(t/2) is f'(t) = 9 - 9csc^2(t/2).
Setting f'(t) = 0, we have 9 - 9csc^2(t/2) = 0. Solving this equation, we get csc^2(t/2) = 1, which means sin^2(t/2) = 1. This gives us sin(t/2) = ±1. The critical points occur when t/2 = π/2 or t/2 = 3π/2. Solving for t, we get t = π or t = 3π as the critical points.
The endpoints of the interval are π/4 and 7π/4.
Now we evaluate the function f at the critical points and endpoints:
From these evaluations, we can see that the absolute maximum value occurs at t = 7π/4 and is approximately 46.607, while the absolute minimum value occurs at t = π/4 and is approximately 6.566.
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Write an equation that can be used to determine the number of hours, h, Hector works given the number of weeks, W.
Enter your equation in the space provided
Part B
Write an equation that can be used to determine Hector's earnings, in dollars, m, for h hours of work.
Enter your equation in the space provided.
Answer:
A). h = 20 w
B). m = 10.5h
Step-by-step explanation:
Part (A).
Let the total number of hours Hector worked = h
And total number of weeks worked by Hector = w
Therefore, number of hours Hector worked in a week =
Since, total number of hours worked in a week = 20
Equation will be,
20 =
h = 20w
Part (B).
Per hour earning of Hector =
m = 10.5h
please help me factorizing above equation
A)4x^3
B)4x^5y
C)8x^5
D)112x^5y
-6
B.
6
C.
20
D.
-20
help help help
Answer:
B. Bertha's dive ended 6 times farther than Vernon's dive.
Step-by-step explanation:
We have that,
Bertha's dive ended -24 m from that starting point.
Vernon's dive ended -4 m from that starting point.
So, we get that,
Bertha's end point = 6 × Vernon's end point
i.e. -24 = 6 × (-4)
So, we see that,
Bertha's dive ended 6 times farther than Vernon's dive.