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Let h be a twice continuously differenti...

Let h be a twice continuously differentiable positive function on an open interval J. Let `g(x) = ln(h(x)` for each `x in J` Suppose `(h'(x))^2 > h''(x)h(x)` for each `x in J`. Then

A

g is increasing on H

B

g is decreasing on H

C

g is concave up on H

D

g is concave down on H

Text Solution

Verified by Experts

The correct Answer is:
D
Given `g(x)=log_(e)(h(x))`
`therefore" "f'(x)=(h'(x))/(h(x))`
`therefore" "g''(x)=(h(x)h''(x)-(h'(x))^(2))/(h^(2)(x))lt0" (given)"`
`therefore" "g''(x)lt0" "rArr" g(x) is concave down"`
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