" (iv) "f(x)=2x-x^(2),x in[0,1]

Verify Lagrange's mean value theorem for the following functions: f(x) = 2x - x^2 , x in [0,1]

Compute the value of 'c' satisfied by the Rolle's theorem for the function . f(x) =x^(2)(1-x)^(2), x in [0,1] .

Verify LMV theorem for f(x)=x^(3)-2x^(2)-x+3 in [0, 1].

Verify mean value theorem for the function f(x) = x^(3)-2x^(2)-x+3 in [0,1]

Verify mean value theorem for the function f(x) = x^(3)-2x^(2)-x+3 in [0,1]

f(x) = x^(3)-2x^(2)-x+3 in [0,1]

Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose the function f is twice differentiable,f(0)=f(1)=0 and satisfies f''(x)-2f'(x)+f(x)gee^(2),x in [0,1] Consider the statements. I. There exists some x in R such that, f(x)+2x=2(1+x^(2)) (II) There exists some x in R such that, 2f(x)+1=2x(1+x)