2 Problem 8. Consider a critical function with power functionexp(0)1+ exp(0)'Show that the power function is increasing. Find the size of this test for testing Ho : 0 < 0 versus Ha : 0 > 0.7(0)0 E R.

Given: Critical function with power function, πθ=expθ1+expθ, θ∈ℝ To show: The power function is…

Answered: Problem 8. Consider a critical function…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 36E

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Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.
If the instantaneous rate of change of f(x) with respect to x is positive when x=1, is f increasing or decreasing there ?
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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Problem 8. Consider a critical function with power function exp(0) T(0) = 1+ exp(0)' 0 E R. Show that the power function is increasing. Find the size of this test for testing Ho : 0 <0 versus Ha : 0 > 0.