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in Continuity and Differentiability by (29.1k points)
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What are the values of ‘a’ for which f(x) = ax is increasing on R?

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Best answer

f(x) = ax

f’(x) = a x log a

\(\because\) f(x) is increasing on R.

\(\therefore\) f’(x) > 0

\(\therefore\) a x log a > 0

\(\because\) Logarithmic function is defined for positive values of a.

\(\therefore\) a > 0

\(\therefore\) ax > 0

\(\because\) ax log a > 0

\(\therefore\) It can be possible when log ax > 0 & log a > 0 or ax < 0 & log a < 0.

log a > 0

\(\therefore\) a > 1

Hence, f(x) is increasing when a > 1.

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