Let f be a function defined on [a, b] such that `f^(prime)(x)>0`, for all `x in (a ,b)`. Then prove that f is an increasing function on (a, b).

Explanation

`text(We have to prove that the function is always increasing i.e.)`


`f(x_1)ltf(x_2)text( for ) x_1ltx_2text( where )x_1,x_2in[a,b]`


`mathbf"PROOF"`


`text(Let ) x_1,x_2 text(be 2 numbers in the interval [a,b] i.e. ) x_1,x_2in[a,b]`


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