This Question: 3 pts 26 of 38 (21 complete) This Test: 100 pls pos An object mov

Question

This Question: 3 pts 26 of 38 (21 complete) This Test: 100 pls pos An object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is given by the function fx)-x3-6 +9x a. Find the instantaneous velocity function v fx) b. Find the velocity when x-1 c. Find the time(s) when v = 0. b, The velocity of the object at x «Ots. (Simplify your answer.) C. The velocity is zero at seconds. (Simplify your answer. Use a comma to separate answers as needed.) Enter your answer in each of the answer boxes

Explanation / Answer

f(x) = x^3 - 6x^2 + 9x

instantenous velocity will be

v = f'(x)

v = 3*x^2 - 2*6*x + 9*1

v = 3x2 - 12x + 9

when x = 1

v = 3*1^2 - 12*1 + 9

v = 3 - 12 + 9 = 0 m/sec

v = 0 m/sec

when v = 0

0 = 3x^2 - 12x + 9

x^2 - 4x + 3 = 0

(x - 3)*(x - 1) = 0

Velocity will be zero when x = 1 and x = 3

The velocity is zero at 1, 3 seconds.

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