In how many points graph of `y=x^3-3x^2+5x-3` intersect the x-axis?

In how many points the graph of f(x)=x^3+2x^2+3x+4 meets the x-axis ?

Following is the graph of y = f' (x) , given that f(c) = 0. Analyse the graph and answer the following questions. (a) How many times the graph of y = f(x) will intersect the x - axis? (b) Discuss the type of roots of the equation f (x) = 0, a le x le b . (c) How many points of inflection the graph of y = f(x), a le x le b , has? ,(d) Find the points of local maxima/minima of y = f(x), a le x le b , , (e) f"(x)=0 has how many roots?

Draw the graph of |y|=(x-1)(x-2)(x-3) .

Draw graph of y=(x^(3)-5x)/(x^(2)+1) .

Prove that graphs y=2x-3 and y=x^2-x never intersect.

Draw the graph of y=(x^(2)-x^(5))(x-2)^(3) .

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

Draw the graph of y=(x^(3))/(3(x+1)) .

The straight line 2x-3y+5=0 intersects the x -axis and y- axis-

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.