By Hastings George Fitzhardinge Berkeley
This Elibron Classics publication is a facsimile reprint of a 1910 version by means of Henry Frowde, London, and so forth.
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Extra resources for Mysticism in modern mathematics
35. 36. Use a graph to estimate the local extrema and inflection points of each function, and to estimate the intervals on which the function is increasing, decreasing, concave up, and concave down. 37. f ( x) x 4 4 x 3 5 38. h( x) x 5 5 x 4 10 x 3 10 x 2 1 39. g (t ) t t 3 41. m( x) x 4 2 x 3 12 x 2 10 x 4 40. k (t ) 3t 2 / 3 t 42. 4 Composition of Functions Suppose we wanted to calculate how much it costs to heat a house on a particular day of the year. The cost to heat a house will depend on the average daily temperature, and the average daily temperature depends on the particular day of the year.
Example 6 Given f (t ) t 2 t , evaluate f (3) and f (2) f (3) 3 2 3 f (2) (2) 2 (2) We could simplify the results above if we wanted to f (3) 32 3 9 3 6 f (2) (2)2 (2) 4 2 6 We are not limited, however, to putting a numerical value as the input to the function. We can put anything into the function: a value, a different variable, or even an entire equation, provided we put the input expression everywhere we see the input variable. Example 7 Using the function from the previous example, evaluate f(a) This means that the input value for t is some unknown quantity a.
We could make an educated guess at a maximum reasonable value, or look up that the maximum circumference measured is 163 feet1. With this information we would say a reasonable domain is 0 c 163 feet. Similarly for the range, it doesn’t make sense to have negative heights, and the maximum height of a tree could be looked up to be 379 feet, so a reasonable range is 0 h 379 feet. Example 2 When sending a letter through the United States Postal Service, the price depends upon the weight of the letter2, as shown in the table below.
Mysticism in modern mathematics by Hastings George Fitzhardinge Berkeley