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- Let f(x) =x² -x - 5 and gx)= -8x+ 4. Find a(3) and flg(3). 9(3) = fig(3)3D %3Dq1= (150-20)/2 - 1/2q2 q2= (150-20)/2 - 1/2q1 Plot these reaction functions in a graph with q1 on the horizontal axis and q2 on the vertical axisFind the natural spline for the data: x0 = 0, x1 = 1, x2 = 2, and f(x0) =1.2, f(x1) = 1.3, f(x2) = 1.0.
- Suppose that while driving a car, the driver suddenly sees an animal standing in the road. The driver's brain registers the information and sends a signal to the driver's foot to hit the brake. The car travels a distance D, in feet, during this time, where D is a function of the speed r, in miles per hour, of the car when the driver sees 13 the animal. That reaction distance is a linear function given by D(r) = 10+ 5. Complete parts a through c below. a) Find the slope of this line and interpret its meaning in this application. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The slope m is |. For each mile per hour faster that the car travels, it takes feet longer to stop. O B. The slope is not defined. For each mile per hour faster that the car travels, it takes 0 foot longer to stop.Suppose the point (5, a) lies on y = f(x), the point (b, c) lies on y = g(x) and the point (2, -8) lies on y = f[g(x)]. The values of a, b, and c are %3D O a = -8, b = 5, c = 2 %3D Oa = 5, b = 8, c 2 %3D a = -8, b = 2, c = 5 Oa = 5, b = 2, c = 8 acer Pane F9 F10 F11If the point (1,4) lies on the graph of y = f(x), then the y-coordinate of the corresponding point on the graph of the transformed function y = 2f(4x) is Answer:
- Decide if the following functions are linearly independent in the interval (-00, 00) f1(2) = 1+r, f2(x) = x, fa(x)=r? %3Dlet x= et then by the chain rule d3x/dx3 equals3. a) Use the Chain Rule and the fact that |x| = Vx2 to show that d %3D dx |x| b) Sketch the graphs of the function f(x) = |x| and its derivative. %3D c) Use the result of part (a) to differentiate the function g(x) = x|x|. Write the derivative as a simplified monomial. %3D
