Let `f(x) = ^3x + px^2 +qx^2 + 6, p,q in R` and `f'(x) lt 0` in largest possible interval `(-5/3,-1)` then value of `q-p` is

Value of p+q for which f(x)=x^(3)+px^(2)+qx+r where p,q,r in R is monotonically decreasing in largest possible interval ((-5)/(3),-1) is

Let f(x)=x^(3) +6x^(2) + px +2 , if the largest possible interval in which f(x) is a decreasing function is (-3,-1) , then the value of p is-

Let f (x) =x ^(3) + 6x ^(2) + ax +2, if (-3, -1) is the largest possible interval for which f (x) is decreasing function, then a=

Let f (x) =x ^(3) + 6x ^(2) + ax +2, if (-3, -1) is the largest possible interval for which f (x) is decreasing function, then a=

f(x) = x^(2) + px + q . If p = 2q and the function has a value of 16 at x = 3, what is the value of p ?

If Rolle's theorem holds for the function f(x) = x^3 + p x^2 + qx + 5, x in [1,3] with c= 2 + (1/ ( sqrt 3 )), find the values of p and q.