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

f has a local maximum at x = a and local minimum at x = b. Then -

Let f(x) be a cubic polynomial which has local maximum at x=-1 \ and \ f(x) has a local minimum at x=1. if f(-1)=10 \ and \ f(3)=-22 , then one fourth of the distance between its two horizontal tangents is ____________

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

Show that (x^5-5x^4+5x^3-1) has a local maximum when x = 1, a local minimum when x = 3, and neither x = 0

Let p(x)be a polynomial of degree 4 having extremum at x = 1,2 and lim_(xrarr0)(1+(p(x))/x^2)=2 Then the value of p(2) is

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.

Let f(x)=x^(3)-3x^(2)+6 find the point at which f(x) assumes local maximum and local minimum.

f(x) is polynomial function of degree 6, which satisfies ("lim")_(x_vec_0)(1+(f(x))/(x^3))^(1/x)=e^2 and has local maximum at x=1 and local minimum at x=0a n dx=2. then 5f(3) is equal to

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

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.