We are told that the function that describes the position of the stone is given by the function
[tex]f(t)=\text{-\lparen t-5\rparen}^2+18[/tex]
recall that the velocity is the derivative of the position. So we need to calculate the derivative. Recall that the derivative of a function of the form
[tex](x\text{ -a\rparen}^2+b[/tex]
where a and b are constants, is
[tex]2(x\text{ -a\rparen}[/tex]
So, applying this, we get
[tex]f^{\prime}(t)=\text{-2\lparen t-5\rparen}[/tex]
we want to find the value of this new function when t=6. So we have
[tex]f^{\prime}(6)=\text{-2\lparen6 -5\rparen= -2}\cdot1=\text{ -2}[/tex]
so when t=6 we have the velocity is -2 m/s. This means that option B is correct.
