app of dy/dx

Q) y ≥ √(1-x²), max( !x!, !y!) ≤ 4
The slope of a family of lines is defined as m(t) = -sin²t + sint + 1, where (t, 2t+0.4) lies inside the region R.

1) The max^mvalue of the slope of any member of family is for t =
(a) 5Î /6 (b) 0.28 (c) 1 (d) None

2) The area of the region R
(a) 8 + Î /2 (b) 4 + Î /2 (c) 8 - Î /2 (d) 4 - Î /2

3) All possible values of 't' lies in
(a) [0.14,1.0] (b) [0.28,0.5] (c) [0.14,0.5] (d) [0.28,1.0]

(need xplanation )