Grade 12Differential Calculus
Ques1) From a fixed point P on the circumference of a circle of radius a , the perpendicualr PR is drawn to the tangent at Q (a variable point). Show that the max area of triangle PQR is [3 (3)1/2 / 8 ] a2.
Ques2) If f '' (x) + f ' (x) + f 2(x) = x 2 be the differential equation of a curve and let P be the point of maxima , then show that the number of tangents which can be drwn from P to x 2 - y 2 is 2.
Ques3) If a differentiable function f (x) has arelative minimum at x = 0, then the function y = f(x) = ax2+bx+c has a relative minimum at x=0, then which of the following is / are correct :-
(a) b = 0 , all a (b) b=0, a> -(1/2) f ' (0) (c) a=0, b=0 (d) a=0 , b=0, c=2.
Ques1) From a fixed point P on the circumference of a circle of radius a , the perpendicualr PR is drawn to the tangent at Q (a variable point). Show that the max area of triangle PQR is [3 (3)1/2 / 8 ] a2.
Ques2) If f '' (x) + f ' (x) + f 2(x) = x 2 be the differential equation of a curve and let P be the point of maxima , then show that the number of tangents which can be drwn from P to x 2 - y 2 is 2.
Ques3) If a differentiable function f (x) has arelative minimum at x = 0, then the function y = f(x) = ax2+bx+c has a relative minimum at x=0, then which of the following is / are correct :-
(a) b = 0 , all a (b) b=0, a> -(1/2) f ' (0) (c) a=0, b=0 (d) a=0 , b=0, c=2.
