In problems 1 and 2 each quotation is a statement about a qu

In problems 1 and 2, each quotation is a statement about a quantity of something changing over time. Let f(t) represent the quantity at time t. For each quotation, tell what f represents and whether the first and second derivatives of f are positive or negative. 1. (a) \"Unemployment rose again, but the rate of increase is smaller than last month.\" (b) \"Our profits declined again, but at a slower rate than last month.\" (c) \"The population is still rising and at a faster rate than last year.\"

Solution

7. here f(x)=(2x-8)^5

take derivative,we get

f\'(x)=5(2x-8)^(5-1)2

=10(2x-8)^4

9. here f(x)=x(3x+7)^5

take derivative ,we get

f\'(x)=(3x+7)^5+x5(3x+7)^(5-1)3

=(3x+7)^5+15x(3x+7)^4

=(3x+7)^4(3x+7+15x)

= (3x+7)^4(18x+7)