If the normal to the curve `y=f(x)` at the point `(3,4)` makes an angle `(3pi)/4` with the positive x-axis, then `f'(3)=` (a) `-1` (b) `-3/4` (c) `4/3` (d) `1`

If the normal to the curve x^(2//3)+y^(2//3)=a^(2//3) makes an angle theta with the x -axis then the slope of the normal is ……….

Determine x so that the line passing through (3,4)a n d(x ,5) makes an angle of 135^0 with the positive direction of the x-axis.

Find the slope of the normal to the curve x=a cos^(3) theta,y=a sin^(3) theta at theta=(pi)/(4) .

The normal to the curve y(x-2)(x-3)=x+6 at the point where the curve intersects the y-a xi s , passes through the point : (1/2,-1/3) (2) (1/2,1/3) (3) (-1/2,-1/2) (4) ((1/(2,1))/2)

If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation ,y(1+x y)dx""=x""dy , then f(-1/2) is equal to: (1) -2/5 (2) -4/5 (3) 2/5 (4) 4/5

Points on the curve f(x)=x/(1-x^2) where the tangent is inclined at an angle of pi/4 to the x-axis are (a)(0,0) (b) (sqrt(3),-(sqrt(3))/2) (-2,2/3) (d) (-sqrt(3),(sqrt(3))/2)

The angle between the tangents to the parabola y^2=4a x at the points where it intersects with the line x-y-a=0 is (a) pi/3 (b) pi/4 (c) pi (d) pi/2

The diagram shows the graph of the derivative of a functin f(x) for 0 le x le 4 with f(0) = 0. Which of the following could be correct statements for y = f(x)? (a) Tangent line to y = f(x) at x = 0 makes an angle of sec^(-1) sqrt 5 with the x - axis. (b) f is increasing in (0, 3). (c) x = 1 is both an inflection point and the point of local extremum. (d) Number of critical point on y = f(x) is two.

The angle between the tangents to the curve y=x^2-5x+6 at the point (2, 0) and (3, 0) is pi/2 (b) pi/3 (c) pi (d) pi/4