find the derivative of the following functions:
(i) f(x) = −x 2 + 10x + 4
(ii) f(x) = 20 − 1 x+2
(iii) f(x) = x 4 e −2x 2
(iv) f(x) = ln(x 2 + 2x + 2).
using the differentiation rules : derivative definition and operation rules (sum, subtraction, multiplication, quotient), derivative of many basic functions (power, quadratic, exponential and natural logarithm functions), function of functions: (chain rule).
explain carefully what rule(s) you have used and where you have applied it(them)

25 ! the line of best fit is h = 5a + 86. predict the height at age 16.

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

Percent increase and decrease. original number: 45 new number: 18