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in Continuity and Differentiability by (29.3k points)
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What are the values of ‘a’ for which f(x) = ax is decreasing on R?

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f(x) = ax

f’(x) = ax log a

\(\because\) f(x) is decreasing on R.

\(\therefore\) f’(x) < 0, ∀ x ∈ R

\(\because\) ax log a < 0, ∀ x ∈ R

\(\because\) Logarithmic function is not defined for negative values of a.

\(\therefore\) ax > 0

\(\therefore\) ax log a < 0 can be possible when log a < 0,∀ x ∈ R.

\(\therefore\) 1 > a > 0

Hence the function f(x), whose values are 1 > a > 0.

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