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 ____________

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

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

The function f(x)=x/2+2/x has a local minimum at (a) x=2 (b) x=-2 (c) x=0 (d) x=1

Let y=f(x) be a polynomial in x. the second order derivative of f(e^x) at x=1 is-

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

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 f(x)=x^(3)+x+1 , let p(x) be a cubic polynomial such that the roots of p(x)=0 are the squares of the roots of f(x)=0 , then

Let f(x)=(x-1)^m(x-2)^n,"x"inR then each critical point of f(x) is either local maximum or local minimum where