Related InterviewSolutions

• A differentiable function `f(x)`has a relative minimum at `x=0.`Then the function `f=f(x)+a x+b`has a relative minimum at `x=0`forall `a`and all`b`(b) all `b`if `a=0`all `b >0`(d) all `a >0`A. all a and all bB. all b if a =0C. all b `gt` 0D. all a `gt` 0
• If `g(x)=max(y^(2)-xy)(0le yle1)`, then the minimum value of g(x) (for real x) isA. `(1)/(4)`B. `3-sqrt3`C. `3+sqrt8`D. `(1)/(2)`
• If the equation `4x^(3)+5x+k=0(k in R)` has a negative real root thenA. k=0B. `-ooltklt0`C. `0ltkltoo`D. `-ooltkltoo`
• An extremum of the function `f(x)=(2-x)/picospi(x+3)+1/(pi^2)sinpi(x+3),0x
• Discuss the extremum of `f(x)=x(x^2-4)^(-1/3)`
• consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1 and `lim_(xrarr0) p(x)/(x^(3))-2=4` Then the value of P(x)_____.
• The funciton f(x)=`x^(2)+(lambda)/(x)`has aA. minimum at x =2 if `lambda` =16B. maximum at x =2 if `lambda` =16C. maximum for no real value of `lambda`D. point of inflectin at x=1 if `lambda`=-1
• Separate the interval of convaity of y =x `log_(e)x-(x^(2))/(2)+(1)/(2)`
• If a function `f(x)`has `f^(prime)(a)=0a n df^(a)=0,`then`x=a`is a maximum for `f(x)``x=a`is a minimum for `f(x)`it is difficult to say `(a)a n d(b)``f(x)`isnecessarily a constant function.A. x=a is a maximum for f(x)B. x=a is a minimum for(x)C. it is difficult to say (a) and (b)D. f(x) is necessarily a constant function
• if `f(x)=4x^3-x^2-2x+1` and `g(x)={min{f(t): 0