InterviewSolution
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InterviewSolution
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Let f be a differentiable function on the open interval(a, b). Which of the following statements must be true? (i) f is continuous on the closed interval [a,b],(ii) f is bounded on the open interval (a,b) |
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Answer» (i)As `f` is a differentiable function in open interval `(a,b)`, it will be continuous in closed interval `[a,b]`. So, statement `(i)` is true. (ii)Statement `(ii)` is not true as we know differentiable function can be non-bounded. Example of this will be `tan theta` between `pi/2 and -pi/2`, is differentiable but is non-bounded. (iii)We are given, `f(a_1) lt 0 ltf(b_1)` and `a_1 lt c lt b_1`, So, there will be definitely a value of `c` where `f(c) = 0` So, this statement will also be true. |
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