Could you please show me the clear and specific steps and answer to solve the questions below?

Thank you so much :)

1)

A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y = -4x2 + 12x. Find the dimensions of the rectangle with the greatest possible area.A particle moves back and forth along a straight line. Its position (in meters), relative to the origin, at any time t (in seconds) is given by s(t) = 3+3 - 9t2 + 5t - 15. Find: (remember to include units) the total distance travelled during the first 10 seconds