9. [-l1 Points] DETAILS TANAPCALC1O 3.1.024. Find the derivative of the function f by using the rules of differentiation. 3 2 X Need Help? 10. [-11 Points] DETAILS TANAPCALC1O 3.1.025. Find the derivative of the function f by using the rules of differentiation. f(x) = 3x4 5x7/2 + 8 f'(x) = 11. [11 Points] TANAPCALC10 3.1.030. Find the derivative of the function by using the rules of differentiation. 2 7 1 f(x)=_+400 x3 x2 x Need Help? 12. [-11 Points] DETAILS TANAPCALC10 3.1.033. Find the derivative of the function f by using the rules of differentiation. 3 5 f(x) = X5 X1/3 13. [-/1 Points] DETAILS TANAPCALC10 3.1.034. Find the derivative of the function by using the rules of differentiation. f ( x ) = 3 + - 3 x f' ( x ) = Need Help? Read It 14. [-/2 Points] DETAILS TANAPCALC10 3.1.042. Find the slope and an equation of the tangent line to the graph of the function f at the specified point. f ( x ) = - _x 2' 2x2 + 8x + 8; (-1, - slope equation y =15. [-/2 Points] DETAILS TANAPCALC10 3.1.046. Let f(x) = x3 - 2x2. Find the points on the graph of f where the tangent line is horizontal. (Enter your answers as a comma-separated list.) smaller x-value (x, y) = larger x-value ( x, y ) = Need Help? Read It 16. [-/3 Points] DETAILS TANAPCALC10 3.1.058.MI. Demand Function for Desk Lamps The demand function for the Luminar desk lamp is given by p = f(x) = -0.1x2- 0.9x + 22 where x is the quantity demanded in thousands and p is the unit price in dollars. (a) Find f'(x). f' ( x) = (b) What is the rate of change of the unit price (in dollars per 1,000 lamps) when the quantity demanded is 7,000 units (x = 7)? $ per 1,000 lamps What is the unit price (in dollars) at that level of demand? $17. [-14 Pomt Di: I AILS TANAFCALC'IO 3.R.047. Let f(x) = 2x3 3x2 74x + 2. (a) Find the points on the graph offat which the slope of the tangent line is equal to 2. (If an answer does not exist, enter DNE.) smaller x-value (X, y) = (|:| ) larger x-value (X, y) = (|:| ) (b) Find the equation(s) of the tangent line(s) of part (a). (Let x be the independent variable and y be the dependent variable. If an answer does not exist, enter Dl' smaller x-value y larger x-value y Need Help? 18. [-14 Points] DETAILS TANAPCALC10 3.R.052. Sales on DSPs The annual sales of digital signal processors (DSPs) in billions of dollars is approximated by 5(t) = 0.14t2 + 0.68t + 3.1 (0 s t s 6) where t is measured in years, with t = 0 corresponding to the beginning of 1997.1' (Round your answers to two decimal places.) (a) What were the sales (in billions of dollars) of DSPs at the beginning of 1997? 515 billion What were the sales (in billions of dollars) at the beginning of 2003? $ billion (b) How fast (in billions of dollars per year) was the level of sales increasing at the beginning of 1997? $ billion/year How fast (in billions of dollars per year) were sales increasing at the beginning of 2003? $ billion/year