Lab Assignment Section 4.9: 1) Use Newton's method to approximate the indicated root of the equation correct to six decimal points. 2x6x\"+3x+1=0 on the interval [2,3]. 2) Explain why Newton's method doesn't work for finding the root of the equation x*=3x+6=0 if the initial approximation is chosen to be x, =1. Lab Assignment Section 4.10 1) Find the most general antiderivative of the function. (Check your answer by differentiation) h(0)=2sin0 sec* 6 2) Findf. a) f"(x): 20x 12x% + 6x b f(x) = 14x3:32x+1 3) A particle is moving with the given data. Find the position function of the particle. a) v(t) =157, s(4)=10 b) a(t)=10sint+3cost, s(0)=0, s(27)=12 4) A company estimates that the marginal cost (in dollars per item) of producing x items is 1.92-0.002x . If the cost of producing one item is $562, find the cost of producing 100 items. ( Marginal cost is the derivative of the cost function) Math 3A Section 4.10 5) A car braked with a constant deceleration of 16 ft/s?, producing skid marks measuring 200 ft before coming to a stop. How fast was the car traveling when the brakes were first applied