Let `f(x) = 6( x-1)^(1/3) -15(x-1)^(2/3) + 12|c|` on the interval `[-7,2]` then which of the following is/are correct?

Let f(x)=(x-1)/(x^(2)) then which of the following is correct?

If the Rolle's theorem is applicable to the function f defined by f(x)={{:(ax^(2)+b",", xle1),(1",", x=1),((c)/(|x|)",",xgt1):} in the interval [-3, 3] , then which of the following alternative(s) is/are correct?

If the Rolle's theorem is applicable to the function f defined by f(x)={{:(ax^(2)+b",", xle1),(1",", x=1),((c)/(|x|)",",xgt1):} in the interval [-3, 3] , then which of the following alternative(s) is/are correct?

Let f(x)=|(1,1,1),(3x-x,5-3x^(2),3x^(3)-1),(2x^(2)-1,3x^(5)-1,7x^(8)-1)| . Then which of the following is/are correct?

The function f(x) = 2x^(3) + 3x^(2) -12 x + 1 decreases in the interval

Let f(x) = (x-1)(x-2)(x-3) on the interval [1,3]. Prove that there is more than one c in (1,3) such that f'©=0

Let f(x) be a differentiable function. If h(x)=(1)/(3) {f(x)}^(3)+{f(x)}^(2)+f(x)+(1)/(3) then which one of the following is correct ?

Let f(x)=(3x-7)x^(2/3) . The interval in which f(x) is increasing.