Let fbe the function defined as follows (a) Find the differential of f (b) Use y
ID: 2888939 • Letter: L
Question
Let fbe the function defined as follows (a) Find the differential of f (b) Use your result from part (a) to find the approximate change in y if x changes from 2 to 1.97. (Round your answer to two decimal places.) (c) Find the actual change in y if x changes from 2 to 1.97 and compare your result with that obtained in part (b). (Round your answer to two decimal places.) 13 points TanApCalc10 3.2.040 My Notes Find the slope m and an equation of the tangent line to the graph of the function fat the specified point. f(x)--(29 r+811 3, -12 points TanApCalc10 3.3.069 My Notes The cumulative number of jobs outsourced overseas by U.S.-based multinational companies in year t from 2005 (t 0) through 2009 is approximated by N(t)0.05(t 1.1)2.2o.7t0.9 (0s t s 4) where N(t) is measured in millions.t How fast was the number of U.S. jobs that were outsourced changing in 2006 (t1)? (Round your answers to the nearest whole number.) jobs per year -12 points TanApCalc10 3.3.012. My Notes Find the derivative of the function. f'(t) = -12 points TanApCalc10 3.1.044 My Notes Find the slope and an equation of the tangent line to the graph of the function fat the specified point. 17 slope equationExplanation / Answer
multiple questions posted.please post each question seperately
1)
given y=f(x)= 4x2-7x+8
(a)
differentiate with respect to x
dy/dx = 4*2x2-1 -7*1 +0
=>dy/dx = 8x-7
=>dy=(8x-7)dx
(b)
x=2, dx=1.97-2=-0.03
dy=(8*2 -7)*(1.97-2)
dy=(16 -7)*(-0.03)
dy=9*(-0.03)
dy=-0.27
(c)
y =f(1.97) -f(2)
y =[4(1.97)2-7(1.97)+8]-[4*22-7*2+8]
y = -0.2664
===============================================================
2)
given y=x2/(x+8)
dy/dx=[2x(x+8) -x2(1+0)]/(x+8)2
dy/dx=[2x2+16x -x2]/(x+8)2
dy/dx=(x2+16x)/(x+8)2
at x = 3
slope ,m=(32+16*3)/(3+8)2
m=(9+48)/112
m=57/121
equation of tangent :
y -(9/11) =(57/121)(x-3)
=>y =(57/121)x-(171/121) +(9/11)
=>y =(57/121)x- (72/121)
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