$\"\"$

The equation is $\"\"$ and the interval $\"\"$ .

Consider $\"\"$ .

Differentiate $\"\"$ on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ is differentiable on the interval $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Substitute $\"\"$ in $\"\"$ .

$\"\"$

From above $\"\"$ and $\"\"$ .

The derivative of the function is an decreasing function.

Hence the function $\"\"$ is an decreasing function.

Any decreasing function crosses the $\"\"$ axis only for one value of $\"\"$ .

Therefore the function $\"\"$ has at most one root in $\"\"$ .

$\"\"$

The equation $\"\"$ has at most one root in $\"\"$ .