Since the deflection at $B$ is zero, you may think that the deflection at $C$ equals

$t_{\frac{C}{B}}.$ This method cannot be used because the slope at $B$

which

means that $t_{\frac{C}{B}}$ is

the deflection at $C.$

is negative, less than

is positive, greater than

is positive, less than

has an unknown sign, not equal to

is negative, greater than