Show that f(x) `= x^5 - 5x^4 + 5x^3 - 1` has a local maximum at x = 1, a local minimum at x = 3 and neither at x = 0

Show that the function f(x) =x^3 +x^2 + x + 1 has neither a maximum value nor a minimum value.

Find the local maximum and local minimum of f(x) = 2 sin x - x in (-pi/2,pi/2)

Discuss the local maximum or minimum of f(x) = x^3 at x = 0

Find the local maximum and local minimumof f(x)=x^(3)-3x in [-2,4].

Prove that the function f(x) = 2x^3 - 6x^2 + 6x + 5 has no maximum or minimum.

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

Let p(x) be a real polynomial of least degree which has a local maximum at x=1 and a local minimum at x=3. If p(1)=6a n dp(3)=2, then p^(prime)(0) is_____

The function f (x) = (x)/(2) + (2)/(x) has a local minimum at :

Show that the function: f(x) = 4x^3 - 18x^2 +27x-7 has neither maximum nor minimum.

If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt x le 2,, and g(x) = int_(0)^(x) f(t ) dt","),( x- e,,"," 2lt x le 3 ,, ""):} x in [ 1, 3 ] , then a. g(x) has local maxima at x=1+log_(e)2 and local minima at x=e b. f(x) has local maxima at x=1 and local minima at x=2 c. g(x) has no local minima d. f(x) has no local maxima