The sum of all integral values of `a` , `a in[1,10]` for which `f(x)=x^(3)-3x^(2)+ax+2cos x` is strictly increasing

Find the values of x for which function f(x)= 2x^(3)-6x^(2) + 6x+24 is strictly increasing.

Find the values of x for which the function f(x)= x^(3)-6x^(2)-36x+ 7 is strictly increasing.

Find the sum of all possible integral values of in [1,100] for which the function f(x)=2x^(3)-3(2+alpha)x^(2) has exactly one local maximum and one local minimum.

The number of integral values of a for which f(x)=x^(3)+(a+2)x^(2)+3ax+5 is monotonic in AA x in R

If all the real values of m for which the function f(x)=(x^(3))/(3)-(m-3)(x^(2))/(2)+mx-2013 is strictly increasing in x in[0,oo) is [0, k] ,then the value of k is,

Find the interval in which 2x^(3)+9x^(2)+12x-1 is strictly increasing.

Find the value of a for which the function f(x) =x^(2)-2ax+6,x gt 0 is strictly increasing.

Find the values of x for which f(x)= 2x^(3)-15x^(2)-144x-7 is (a) Strictly increasing (b) strictly decreasing

The function f(x)=x^(3)+6x^(2)+(9+2k)x+1 is strictly increasing for all x if

Find the interval in which f(x)=x^(3)-3x^(2)-9x+20 is strictly increasing or strictly decreasing.