Ques1) The eqn of tangen to the curve y = cos(x+y) where -2pie ≤ x ≤ 2 pie, that are parallel to the line x+2y = 0
(a) x+2y = pie/2 and x+2y = -3 pie/2
(b) x+2y = pie/2 and x+2y = 3 pie/2
(c) x+2y = 0 and x+2y = pie
(d) none of these
Ques2) Show that the no. of solutions of the eqn
x3 + 2x2 + 5x +2 cosx = 0 in [0, 2 pie] is 0.
Ques3) The tangents are drawn from the points of straight line 3x + 4y = 24 to the curve x 2 + (y 2 / 4) = 1. Then show that the curve passes through a fixed point which lies on 16x -3y = 0.
106Q2. f(x) = x3+2x2+5x+2cosx
f'(x) = 3x2+4x+5-2sinx
Now min value of 3x2+4x+5 is (4.5.3-16)/12 = 11/3 = 3.67
So f'(x) is always positive
So f(x) is an increasing function
So in the interval [0,2∩] its min value will be at x=0
At x=0 f(x) = 2
So in the given interval for no value of x is f(x) zero so no solution
