Answer the following questions in each picture.

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.) f(x) = 7 - 3x Step 1: f ( x + h ) = 7 - 3( xth) X Step 2: f ( x + h) - f(x) = 7 - 3(xth) - (7-3x) x Step 3: f (x + h) - f(x) h Step 4: f'(x) = lim f ( x + h) - f(x) h - C hAt a temperature of 20C, the volume V (in liters) of 1.33 g of 02 is related to its pressure p (in atmospheres) by the formula V(p) = 1 p (a) What is the average rate of change of V with respect to p as p increases from p = 7 to p = 8? -1/56 L/atm (b) What is the rate of change to V with respect to p when p = 7? x L/atm 5. [-l1 Points] TANAPCALC10 2.6.034. Cost of Producing Surfboards The total cost C(x) (in dollars) incurred by Aloha Company in manufacturing x surfboards a day is given by the following function. C(x) = 8x2 + 500x + 130 where (o s x s 15) (a) Find C'(x). C'(x) = (b) What is the rate of change of the total cost (in dollars) when the level of production is 7 surfboards a day? 1; per surfboard 6. [-/0.5 Points] DETAILS TANAPCALC10 3.1.004. MY NOTES Find the derivative of the function f by using the rules of differentiation. f (x) = x8 f' ( x ) = 7. [-/0.5 Points] DETAILS TANAPCALC10 3.1.006. MY NOTES Find the derivative of the function f by using the rules of differentiation. f (x) = x0.7 f' ( x ) = 8. [-/0.5 Points] DETAILS TANAPCALC10 3.1.011. MY NOTES Find the derivative of the function f by using the rules of differentiation. f(x) = 20x1/4 f' ( x ) =9. [-/0.5 Points] DETAILS TANAPCALC10 3.1.014.MI. MY NOTES Find the derivative of the function by using the rules of differentiation. F ( u) = Vu f' ( u ) = 10. [-/1 Points] DETAILS TANAPCALC10 3.1.018. MY NOTES Find the derivative of the function f by using the rules of differentiation. f(x) = 2x3 - 6x2 + 7 f' ( x ) = 11. [-/1 Points] DETAILS TANAPCALC10 3.1.023. MY NOTES Find the derivative of the function f by using the rules of differentiation. f(x) = 8x5 - 3x2 + 7 X f'( x ) =12. [-11 Points] TANAPCALC10 3.1.050. A straight line perpendicular to and passing through the point of tangency of the tangent line is called the normal to the curve. Find an equation of the tangent line and the normal to the curve y = X3 3x + 5 at the point (2, 7). (Let x be the independent variable and y be the dependent variable.) tangent line y normal line y = 13. [-11 Points] TANAPCALC10 3.1.058.MI. Demand Function for Desk Lamps The demand function for the Luminar desk lamp is given by l p=f(X)=0.lx20.ZX+26 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 2,000 units (x = 2)? $ per 1,000 lamps What is the unit price (in dollars) at that level of demand? $