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Statement 1: If g(x) is a differentiable...

Statement 1: If `g(x)` is a differentiable function, `g(2)!=0,g(-2)!=0,` and Rolles theorem is not applicable to `f(x)=(x^2-4)/(g(x))in[-2,2],t h e ng(x)` has at least one root in `(-2,2)dot` Statement 2: If `f(a)=f(b),t h e ng(x)` has at least one root in `(-2,2)dot` Statement 2: If `f(a)=f(b),` then Rolles theorem is applicable for `x in (a , b)dot`

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Statement 1: If g(x) is a differentiable function, g(2)!=0,g(-2)!=0, and Rolles theorem is not applicable to f(x)=(x^2-4)/(g(x)), x in[-2,2],then g(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b),t h e ng(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b), then Rolles theorem is applicable for x in (a , b)dot

Rolle's theorem is not applicable to f(x) = |x| in [ -2,2] because

Rolle's theorem is not applicable to f(x) = |x| in [ -2,2] because

Statement I If g(x) is a differentiable function g(1) ne0, g(-1)ne0 and Rolle's theorem is not applicable to f(x)=(x^(2)-1)/(g(x)) in [-1, 1] , then g(x) has atleast one root in (-1, 1) . Statement II if f(a)=f(b) , then Rolle's theorem is applicable for x in (a, b) .

Rolle's theorem is applicable for the function f(x) = |x-1| in [0,2] .

Rolle's theorem is applicable for the function f(x) = |x-1| in [0,2] .

prove that the roll's theorem is not applicable for the function f(x)=2+(x-1)^((2)/(3)) in [0,2]

Fill in the blanks: Rolle's Theorem is not applicable to the function f(x) = (x-1)^(2//3) on [0,2] as f is not derivable at ………… .

If f(x)={{:(x,olexle1),(2-x,1lexle2'):} then Rolle's theorem is not applicable to f(x) because

Let f(x)a n dg(x) be two differentiable functions in R a n d f(2)=8,g(2)=0,f(4)=10 ,a n dg(4)=8. Then prove that g^(prime)(x)=4f^(prime)(x) for at least one x in (2,4)dot