Question

If f(x)=x^3/2 then f'(4)=

Answer 1

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