What are the values of ‘a’ for which f(x) = ax is increasing on R?
f(x) = ax
f’(x) = ax log a
f(x) is increasing on R.
f’(x) > 0
ax log a > 0
Logarithmic function is defined for positive values of a.
a > 0
ax > 0
ax log a > 0
It can be possible when log ax > 0 & log a > 0 or ax < 0 & log a < 0.
log a > 0
a > 1
Hence, f(x) is increasing when a > 1.