if a function f(x) is
(i) continuous on [a,b]
(ii) derivable on (a,b) and
(iii) f(x) `gt 0 x in (a,b)` then show that f(x) is strictly increasing on [a,b]

Show that the function f(x) = 2x+1 is strictly increasing on R.

Show that the function f(x)=a^x ,\ a >1 is strictly increasing on Rdot

Show that the function f(x)=a^x ,\ a >1 is strictly increasing on Rdot

Show that the function f(x)=x^(2) is a strictly increasing function on (0,oo).

Function f(x)=a^x is increasing on R , if (a) a >0 (b) a 1

If the functions f(x) and g(x) are continuous on [a,b] and differentiable on (a,b) then in the interval (a,b) the equation |{:(f'(x),f(a)),(g'(x),g(a)):}|=(1)/(a-b)=|{:(f(a),f(b)),(g(a),g(b)):}|

Let f is continuous on [a, b] and differentiable on (a,b)s.t.t^2(a)-t^2(b)=a^2-b^2. Show that ... f(x) f prime (x) = x has atleast one root in (a, b).

Let f: [a, b] -> R be a function, continuous on [a, b] and twice differentiable on (a, b) . If, f(a) = f(b) and f'(a) = f'(b) , then consider the equation f''(x) - lambda (f'(x))^2 = 0 . For any real lambda the equation hasatleast M roots where 3M + 1 is

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).

Without using the derivative show that the function f(x)=7x-3 is strictly increasing function on R .