Verify Rolle's theorem for `f(x) = x^2 +2X-8 on [-4,2]`

Verify Rolle's theorem for (i) f(x) =x^2-5x+4 on [1,4]

Discuss the applicability of Rolle's theorem to the function f(x)=x^(2)+1" on "[-2,2] .

Show that the Rolle's theorem is not applicable for f(x) = x^(1/3) on [-1,1]

Factorise the following : x^2 + 2x - 8

Verify Lagrange's mean value theorem for the function f defined by f (x) = x^2 + x - 1 in the interval [0,4] .

Factorise the following : 5x^2 - 8x - 4