F(theta) = cos theta/1 + sin theta g(x) = 8 Squareroot x + 6 tan(x^4 + 1) An obj
ID: 2883568 • Letter: F
Question
F(theta) = cos theta/1 + sin theta g(x) = 8 Squareroot x + 6 tan(x^4 + 1) An object moving along a straight line has a displacement at time t given by the formula s(t) = t^3 - 9t^2 + 24t + 2 (where s is in meters and t is in seconds.) (a) Find the velocity and acceleration functions at time t. (b) Find the times when the velocity is zero. (c) On what time intervals is the velocity positive and on what time intervals is it negative? (a) Find the equation of the tangent line for the function f(x) = 1 - 2x + 4x^2 at the with coordinates (1, 3) b) Find dy, if y = 1 - 2x + 4x^2, x = 1 and dx = 0.27. Give your answer to two places.Explanation / Answer
From the given question,
(a)displacement=s(t) = t3 -9t2+24t+2
velocity=v(t)=3t2 -18t +24
acceleration=a(t)=6t -18
(b) times when velocity is zero,
3t2 -18t +24 =0
3( t2 -6t +8) =0
(t-2)(t-4)=0
t=2 sec, t=4 sec
(c) v= (t-2)(t-4)
velocity is positive when 0<t<2, and t>4
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