# Explain, please?

If the distance of a particle from the origin on a line is given by x(t)=3+(x-2)^4, then the number of times the particle reverses its direction is

Answers: 0 or 1 or 2 or 3

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- Wayne DeguManLv 76 months ago
x(t) = 3 + (t - 2)⁴

so, v(t) => x'(t) = 4(t - 2)³

The velocity is zero when x = 2

For t < 2, v(t) < 0

and for t > 2, v(t) > 0

Hence, for 0 ≤ t < 2, particle goes in negative direction

for t = 2, particle is stationary

for t > 2. particle goes in positive direction

i.e. changes direction once.

:)>

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