Let f ( x ) be continuous on [ a , b ] and differentiable on ( a , b ) . Number of correct statements among the following: Statement I:

Question

$Let$ $f (x)$ $be continuous on$ $[a, b]$ $and differentiable on$ $(a, b)$ .

$Number of correct statements among the following:$

$Statement I: If f (x) is strictly increasing on (a, b), then f^{1} (x) > 0 for all x \in (a, b) .$

$Statement II: If f (x) is strictly decreasing on (a, b), then f^{1} (x) < 0 for all x \in (a, b) .$

$Statement III: f (x) and f^{1} (x) have opposite sign, for all x, then f^{2} (x) is a decreasing function.$

$Statement IV: f (x) and f^{1} (x) have opposite sign, for all x, then$ $| f (x) |$ $is an increasing function.$

Smart Achievers · Accepted Answer

(2)

$f (x)$

$Statement-III: (f^{2} {(x))}^{1} = 2 f (x) f' (x) = - v e$

$Statement-IV:$

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