MA 223 Exam 2 Spring 20071. Find f0:f(x)=3x2− x +42x − 1A. f0(x)=6x2− 10x +9(2x − 1)2B. f0(x)=6x2− 6x − 7(2x − 1)2C. f0(x)=−6x2+10x − 9(2x − 1)2D. f0(x)=−6x2+6x +7(2x − 1)2E. f0(x)=−6x2− 10x +9(2x − 1)22. Find y0if y =2(2x3− x)(x2+4).A. y0=4x5+14x3− 8xB. y0=14x4− 4x2+23x − 4C. y0=24x3− 4xD. y0=6x4+23x − 4E. y0=20x4+42x2− 8MA 223 Exam 2 Spring 20073. Find the derivative:f(x)=5x +21+3x4A. f0(x)=44(5x +2)3(3x +1)6B. f0(x)=−4(5x +2)3(3x +1)6C. f0(x)=44(5x +2)3(3x +1)5D. f0(x)=−4(5x +2)3(3x +1)5E. f0(x)=−44(5x +2)3(3x +1)64. Find the equation of the line tangent to the graph of f (x)=1+2√x3+1whenx =2.A. y =4x − 1B. y =13x +193C. y =4x +1D. y =13x −233E. y =4x − 15MA 223 Exam 2 Spring 20075. Find the slope of the line tangent to the graph of the function f defined by the equation below, atthe point (−1, 1).x + y − x2y3+1=0A.32B. −17C. 0D. −12E. 86. Find the x-coordinate only of any point(s) where the tangent line to the graph of f is horizontal.f(x)=(x2− 2)(2x +1)A. x = −1,x=32B. x = −1,x=23,x=32C. x = −1,x =0,x =23D. x = −1,x=23E. x = −1,x =0,x=32MA 223 Exam 2 Spring 20077. Let f and g be functions that are differentiable at x =3. Findh0(3) if f(3)=2,g(3) = −3,h(3) =72,f0(3) = −1,g0(3) = 5 andh(x)=f(x) − x21+g(x)A. −75B.494C. −76D.554E. −748. Find f00(1) if f(x)=(x2− 7)3.A. −38B. 216C. −144D. 72E. −36MA 223 Exam 2 Spring 20079. The distance s (in feet) covered by a car after t seconds is given by s(t)=−t3+15t2+8t.Findthecar’s velocity after 3 seconds.A. 132 ft/secB. 12 ft/secC. 71 ft/secD. 15 ft/secE. 63 ft/sec10. Use differentials to estimate3√11.2. Round your answer to 4 decimal places.A. 2.2131B. 2.6235C. 2.2374D. 2.6720E. 2.2667MA 223 Exam 2 Spring 200711. One hour after x milligrams of a particular drug are administered to a patient, the change in bodytemperature is given by the function below. Find the rate at which the body temperature is changingwhen 4 milligrams are administered.T (x)=x2(1 −x9)A.809degrees per mgB.83degrees per mgC.269degrees per mgD.409degrees per mgE.13degree per mg12. Let P be the profit function for the sale of an item. Which of the following would represent anestimate of the profit from the sale of the 10thunit, when 9 units have been sold?A. P0(10) − P0(9)B. P0(9)C. P0(10) − P (9)D. P0(10)E. P (10) − P0(9)MA 223 Exam 2 Spring 200713. When the price of a certain commodity is p dollars per unit, consumers demand x hundred units ofit monthly, where75x2+17p2=5, 375How fast is the demand x increasing with respect to time when the price is $10 and is decreasing atthe rate of 75 cents per month? (Round your answer to the nearest unit per month.)A. 2, 267 units per monthB. 536 units per monthC. 35 units per monthD. 1, 700 units per monthE. 243 units per