A polynomial function P(x) of degree 5 with leading coefficient one, increases in the interval `(-oo, 1 )` and `(3,oo)` and decreases in the interval ( 1 , 3). Given that P(0) = 4 and P'(2)=0. Find th value P'(6).

Find a polynomial f(x) of degree 4 which increases in the intervals (-oo,1) and (2,3) and decreases in the intervals (1,2) and (3,oo) and satisfies the condition f(0)=1

Find a polynomial f(x) of degree 5 which increases in the interval (-infty, 2] and [6, infty) and decreases in the interval [2,6]. Given that f(0) = 3 and f'(4)-0 .

Show that f(x)=1/(1+x^2) decreases in the interval [0,\ oo) and increases in the interval (-oo,\ 0] .

y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(1) = -8, then the value of f(2) is

y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(1) = -8, then the value of f(2) is

y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(1) = -8, then the value of f(2) is

y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(x)=0 has four real roots, then the range of values of leading coefficient of polynomial is

y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(x)=0 has four real roots, then the range of values of leading coefficient of polynomial is