first you have to find the derivative of the equation f(x)=[tex] x^{3/2} [/tex] . To do this, you can use the power rule ([tex]f(x)= x^{n}[/tex] goes to [tex]f'(x)=nx^{n-1} [/tex]). so the derivative would be f'(x)= [tex] \frac{3}{2} x^{ \frac{3}{2}-1 } [/tex] , which can be written as f'(x)= [tex] \frac{ 3\sqrt{x}}{2} [/tex]. then you plug in 4 for x, and get [tex] \frac{3 \sqrt{4} }{2} =3[/tex], so f'(x)=3
