Show that `f(x)=x^2+(250)/x` has a local minimum at x=5.

Show that f(x)=3x-x^3 has a local maximum at x=1.

If the function f(x) = x^(2) + alpha//x has a local minimum at x=2, then the value of alpha is

The function f(x)=(x)/(2)+(2)/(x) has a local minimum at x=2( b) x=-2x=0 (d) x=1

The function f(x)=x^(3)-ax has a local minimum at x=k , where k ge 2, then a possible value of a is

Show that f(x)=1+x+x^2+x^3 has no local extremum.

Let f(x) be a polynomial of degree 3 having a local maximum at x=-1. If f(-1)=2,\ f(3)=18 , and f^(prime)(x) has a local minimum at x=0, then distance between (-1,\ 2)a n d\ (a ,\ f(a)), which are the points of local maximum and local minimum on the curve y=f(x) is 2sqrt(5) f(x) is a decreasing function for 1lt=xlt=2sqrt(5) f^(prime)(x) has a local maximum at x=2sqrt(5) f(x) has a local minimum at x=1

Show that f(x)=x^3-3x^2+15x+2 has no local extremum.

Let f and g be two differentiable functions defined from R->R^+. If f(x) has a local maximum at x = c and g(x) has a local minimum at x = c, then h(x) = f(x)/g(x) (A) has a local maximum at x = c (B) has a local minimum at x = c (C) is monotonic at x = c 1.a g(x) (D) has a point of inflection at x = c