If `p(x)` is a polynomial of degree 3 satisfying `p(-1)=10 , p(1) =-6 and p(x)` has maxima at `x=-1 and p'(x)` has minima at `x=1,` find the distance between the local maxima and local minima of the curve.

If P(x) be a polynomial of degree 3 satisfyints P(-1)=10,P(1)=-6 and P(x) has maximum at x =-1 and P (x)has minima at x=1 lf the distance between local maximum and local minimum of the curve is Ksqrt65 find K.

Determine the local maxima and local minima of f(x)=(x+1)^2(x-1)^3 is

Determine the local maxima and local minima of f(x)=x^3-6x^2+12x-8 is

f(x) is cubic polynomial with f(x)=18 and f(1)=-1 . Also f(x) has local maxima at x=-1 and f^(prime)(x) has local minima at x=0 , then (A) the distance between (-1,2)a n d(af(a)), where x=a is the point of local minima is 2sqrt(5) (B) f(x) is increasing for x in [1,2sqrt(5]) (C) f(x) has local minima at x=1 (D)the value of f(0)=15

Show that the function f(x)=4x^3-18x^2+27x-7 has neither local maxima and local minima

Find the local maxima and local minima for the given function and also find the local maximum and local minimum values f(x) = x^3−6x^2+9x+15

Find the point of maxima and minima for the function 2x^3-9x^2+100

If P(x) is a polynomial of the least degree that has a maximum equal to 6 at x=1 , and a minimum equal to 2 at x=3 , then int_(0)^(1)P(x)dx equals

If p(x) be a polynomial satisfying the identity p(x^2)+2x^2+10x=2xp(x+1)+3 , then p(x) is given by

If p(x) be a polynomial such that p(-a/b)=0 , then one of the factor of p(x) is