II. Differentials Recall, the DERIVATIVE values represent SLOPE values on a given function. Slope = Derivative = The quantities, dy and dx are called “differentials”, and represent small, nonzero values for the changes in y and x. Specifically, if y=f(x), then Differentials are used to approximate changes in the output values of a function given small changes in the input values. THIS IS REALLY JUST THE SAME AS UTILIZING LINEAR APPROXIMATIONS, but allows us to shortcut the process of writing the equation of the line.

II. Differentials Recall, the DERIVATIVE values represent SLOPE values on a given function. Slope = Derivative = The quantities, dy and dx are called “differentials”, and represent small, nonzero values for the changes in y and x. Specifically, if y=f(x), then Differentials are used to approximate changes in the output values of a function given small changes in the input values. THIS IS REALLY JUST THE SAME AS UTILIZING LINEAR APPROXIMATIONS, but allows us to shortcut the process of writing the equation of the line.

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.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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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.