Let f(x)`=x^(3) +3(a-7)x^(2)+3(a^(2) -9) x-1.` If f(x) has positive point of maxima then find possible values of 'a'

The value of a for which x^(3)+3(a-7)x^(2)+3(a^(2)-9)x-2 has a + ve point of maxima

Let f(x)=3x^(3)+7x^(5) . Find f^(')(2) .

Let f(x)=a/x+x^2dot If it has a maximum at x=3, then find the value of adot

Let f(x) =x^(3) =x^(2) -x-4 (i) find the possible points of maxima // minima of f(x) x in R (ii) Find the number of critical points of f(x) x in [1,3] (iii) Discuss absolute (global) maxima // minima value of f(x) for x in [-2,2] (iv) Prove that for x in (1,3) the function does not has a Global maximum.

Let f(x)=x^(3)-3x^(2)+2x. If the equation f(x)=k has exactly one positive and one negative solution then the value of k equals.-(2sqrt(3))/(9)(b)-(2)/(9)(2)/(3sqrt(3)) (d) (1)/(3sqrt(3))

Let f(x)=x^(3)/3-x^(2)/2+x-16 . Find f^(')(0), f^(')(-1) .

If the function f(x)=(a+3)x^(3)+(a-3)x^(2)+4(a-4)x+5 has maxima at some x in R^(-) and a minima at some x in R^(+), find the possible values of a.

Let f:R rarr R be defined by, f(x)={[k-x;x le-1],[x^(2)+3,,xgt-1] .If f(x) has least value at x=-1 , then the possible value of k is