$\"\"$

The beam deflection is $\"\"$ .

Where $\"\"$ is length of the beam.

$\"\"$

Apply derivative with respect to $\"\"$ .

$\"\"$

Find the relative extremas by equating the first derivative to zero.

$\"\"$

Find the maximum deflection using second derivative test.

$\"\"$

Apply derivative with respect to $\"\"$ .

$\"\"$

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

$\"\"$ .

So the function has minimum value at $\"\"$ .

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

$\"\"$

So the function has maximum value at $\"\"$ .

$\"\"$

The function has maximum value at $\"\"$ .