A particle moves along the x-axis so that at time t≥0 its position is given by x(t) = t³-42t²+81t. Determine all intervals when the speed of the particle is increasing.

answer: the correct option is d.

explanation:

it is given that the triangle j'k'l' shown on the grid below is a dilation of triangle jkl using the origin as the center of dilation.

from the given graph it is noticed that k(4,8) and k'(2,4). let origin is defined by o and scale factor is defined by k, then

    (1)

distance formula,

put these values in equation (1).

therefore scale factor is     and option d is correct.

the graph g(x) is f(x) translated 7 units in the negative y direction and translated 2 units in the negative x direction