Let `P(x)` be a polynomial of least degree whose graph has three points of inflection `(-1,-1),(1.1) `and a point with abscissa 0 at which the curve is inclined to the axis of abscissa at an angle of `60^@.` Then find the value of`int_0^1 p(x)dx.`

Consider a polynomial y = P(x) of the least degree passing through A(-1,1) and whose graph has two points of inflection B(1,2) and C with abscissa 0 at which the curve is inclined to the positive axis of abscissa at an angle of sec^(-1)sqrt(2) The value of P(0) is

Consider a polynomial y = P(x) of the least degree passing through A(-1,1) and whose graph has two points of inflection B(1,2) and C with abscissa 0 at which the curve is inclined to the positive axis of abscissa at an angle of sec^(-1)sqrt(2) The value of P(2) ius

Consider a polynomial y = P(x) of the least degree passing through A(-1,1) and whose graph has two points of inflection B(1,2) and C with abscissa 0 at which the curve is inclined to the positive axis of abscissa at an angle of sec^(-1)sqrt(2) The equation P(x) =0 has

The tangent to the graph of the function y=f(x) at the point with abscissa x=a forms with the x-axis an angle of pi/3 and at the point with abscissa x=b at an angle of pi/4 , then the value of the integral, int_1^b f'(x).f'' (x) dx is equal to

The tangent to the graph of the function y=f(x) at the point with abscissa x=a forms with the x-axis an angle of (pi)/(3) and at the point with abscissa x=b at an angle of (pi)/(4) then the value of the integral,int_(1)^(b)f'(x)*f''(x)dx is equal to

Let p(x) be a real polynomial of least degree which has a local maximum at x=1 and a local minimum at x=3. If p(1)=6 and p(3)=2, then p'(0) is