Let `f(x) = 2x^3 + 3(1-3a)x^2 + 6(a^2-a)x +b` where `a, b in R`. Find the smallest integral value of a for which f(x) has a positive point of local maximum.

Consider three real-valued functions f,g and h defined on R( the set of real numbers).Let f(x)=2x^(3)+3(1-(3a)/(2))x^(2)+3(a^(2)-a)x+b where a,b in R and g(x)=(f'(x))/(6). The true set of values of a for which f(x) has negative point of local minimum,is

let f(x)=2x^(3)-3(a-3)x^(2)+6ax+a+2 where a in R the set of values of a for which f(x) has no point of extrema is (A)(1,10)(B)(2,7)(C)(3,10)(D)(8,9)

Find the values of x for which f(x) = x^4+2x^3-2x^2-6x+5 is locally maximum and minimum.

Given f(x)={(x^(2)-4|x|+a ,if, x le 2),(6-x, if, x gt 2):} ,then number of positive integral values of a for which f(x) has local minima at x=2 .

Let f:R rarr R be defined as f(x)={2kx+3,x =0 If f(x) is injective then find the smallest integral value of

Let f(x)={x^(2)-2|x|+a,x<=1 and 6+x,x<1 number of positive integral value(s) of 'a' forwhich f(x) has local minima at x=1 is/are

Let f(x) = x^(3)-3(7-a)X^(2)-3(9-a^(2))x+2 The values of parameter a if f(x) has a positive point of local maxima are

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

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