1. for what values if x does the graoh of f(x)= 6x^3-45x^2+72x+36have a horizont

Question

1. for what values if x does the graoh of f(x)= 6x^3-45x^2+72x+36have a horizontal tangent? wnter the x values in order, smallestfirst, to 4 places of accuracy. x1= less then equal tox2 7. let f(x) = 3x^6sqaure root of x + (-5/x^2 sqaure root of x) f ' (x) =
12. a particle moves along a straight line and its position attune t is given by s(t) = 2t^3 - 18t^2+30t where s is measures in feet and t in seconds. find the velocity (inft/sec) of the particle at time t = 0; ??? the particle stops moving ( i. e is in a rest) twice, oncewhen t = A and again when t = B where A<B. A is ?? and Bis??? what is the position of the particle at time 12?
finally, what is the total distance the particle travelsbetween time 0 and time 12?
7. let f(x) = 3x^6sqaure root of x + (-5/x^2 sqaure root of x) f ' (x) = 12. a particle moves along a straight line and its position attune t is given by s(t) = 2t^3 - 18t^2+30t where s is measures in feet and t in seconds. find the velocity (inft/sec) of the particle at time t = 0; ??? the particle stops moving ( i. e is in a rest) twice, oncewhen t = A and again when t = B where A<B. A is ?? and Bis??? what is the position of the particle at time 12?
finally, what is the total distance the particle travelsbetween time 0 and time 12?

Explanation / Answer

#7 f(x)= 3x6(x) +(-5/x2)(x) before you start differentiating, you need to pull the liketerm out in front of equation... so the like term in this equationwould be (x) f(x)= x( 3x6 +(-5/x2) to find f '(x), you need to use the product rule which statesthis; f(x) times g '(x) + g(x) times f '(x) f '(x)= x( 18x5 + 10x-3) +(3x6 -5/x2)(.5x-.5)..... which is theanswer #12 s(t)= 2t3 - 18t2 + 30t to find the velocity, you'll need to find s '(t) which equalsv(t). s'(t) or v(t)= 6t2 -36t + 30 to find the velocity at time = 0, you just have to plugin 0 for t in the v(t) equation. Answer should be 30ft/sec. to find the position particle at time = 12, you just have toplug in 12 for t in the s(t) equation. Answer should be 1,224ft. for the final part, the answer would be 1,224 ft. This is dueto the fact that when t=0 the position is 0. so when you add 0 and1,224 (for time of 12 secs) you get 1,224 ft. I hope this helps(=

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