1. for what values if x does the graoh of f(x)= 6x^3-45x^2+72x+36have a horizont
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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 2. find the derivative of the function g(x) = (2x^2-5x-5) e^x g ' (x) = 3. find the derivative of the function g(x)= e^x/ 2+4x find g'(x) = 4. if f(x)= (7x^2-6)(3x+2), find f '(x) find f'(1)= 5. if f(t)= square root of 7 / t^6, find f ' (t) = 6. if f(x) = 6x+3/7x+6, find f ' (x) and f '(3). 7. let f(x) = 3x^6sqaure root of x + (-5/x^2 sqaure root of x) f ' (x) = 8. if f(x) = 6x+2/7x+3 find f ' (3) 9. if f(x) = 4x^2+3x+4/ sqare root of x, find f ' (x) , and f' (3) 10. let f(x) = 2x+3-7e^x. then the equation of thetangent line to the graoh of f(x) at the point (0, -4), is given byy = mx+b where m = and b = 11. a particle moves along a straight line with equation ofmotion s = t^6 -5t^5. find the value of t (other than 0) at whichthe acceleration is eqaul to zero. 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? 13. if a ball is thrown vertically upward from the roof of 48foot building with a velocity of 32 ft/sec, then what is themaximum height the ball reaches? what is the velocity of the ball when it hits theground?
2. find the derivative of the function g(x) = (2x^2-5x-5) e^x g ' (x) = 3. find the derivative of the function g(x)= e^x/ 2+4x find g'(x) = 4. if f(x)= (7x^2-6)(3x+2), find f '(x) find f'(1)= 5. if f(t)= square root of 7 / t^6, find f ' (t) = 6. if f(x) = 6x+3/7x+6, find f ' (x) and f '(3). 7. let f(x) = 3x^6sqaure root of x + (-5/x^2 sqaure root of x) f ' (x) = 8. if f(x) = 6x+2/7x+3 find f ' (3) 9. if f(x) = 4x^2+3x+4/ sqare root of x, find f ' (x) , and f' (3) 10. let f(x) = 2x+3-7e^x. then the equation of thetangent line to the graoh of f(x) at the point (0, -4), is given byy = mx+b where m = and b = 11. a particle moves along a straight line with equation ofmotion s = t^6 -5t^5. find the value of t (other than 0) at whichthe acceleration is eqaul to zero. 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? 13. if a ball is thrown vertically upward from the roof of 48foot building with a velocity of 32 ft/sec, then what is themaximum height the ball reaches? what is the velocity of the ball when it hits theground?
Explanation / Answer
11. s=t^6 - 5t^5 acceleration is s" so s'=6t^5-25t^4 s"=30t^4-100t^3 set s"=0 since acceleration is zero 0=30t^4-100t^3 0=t^3(30t-100) t=0 30t=100 t=10/3=3.33
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