e ƒ(x)=—, given ƒ'(x)= €*(x−1), ƒ *(x) = e* (x² -2x+2) x² Analyze the function f(x) = i) Domain and range ii) Intercepts 3 X = €² based on the following headings: X iii) Critical points and determine if they are local max., local min. or neither. iv) Intervals of increase and decrease v) Points of inflection vi) Intervals of concavity vii) Sketch the function

What is the purpose of the Intermediate Value Theorem?

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 xis large, which function grows faster, f(x)=2x or g(x)=x2?