Prove that graphs `y=2x-3a n dy=x^2-x` never interest.

Prove that graphs of y=x^2+2a n dy=3x-4 never intersect.

The graph y=2x^3-4x+2a n dy=x^3+2x-1 intersect in exactly 3 distinct points. Then find the slope of the line passing through two of these points.

Draw the graph of |y|=|2^|x|-3| .

In how many points graph of y=x^3-3x2+5x-3 interest the x-axis?

Sketch the region bounded by the curves y=x^2a n dy=2/(1+x^2) . Find the area.

In what ratio does the x-axis divide the area of the region bounded by the parabolas y=4x-x^2a n dy=x^2-x ?

Prove that for all real values of xa n dy ,x^2+2x y+3y^2-6x-2ygeq-11.

Which of the following pair of graphs intersect? y=x^2-xa n dy=1 y=x^2-2x +3 and y=sinx y=x^2-x+1a n dy=x-4

Draw the graph of y = |x^(2) - 2x|-x .

The area bounded by the curves y=x(x-3)^2a n dy=x is________ (in sq. units)