Can anyone show me how to find e.g $\phi(1,−1,−2)$, given the scalar field $\phi(x,y,z) = 4yz^{3}+ 3xyz−z^{2}+ 2$?

Question

I have a question in my applied calculus worksheet that I don't know how to work out.

Given the scalar field $\phi(x,y,z) = 4yz^{3}+ 3xyz−z^{2}+ 2$. I need to find:
(i)$\phi(1,−1,−2)$
(ii)$\phi(0,−3,1)$
(iii)$\phi(1,2,3)$

Does anyone know how does one do this?

Thanks

Aigars

Answer 1

Just note that $$\phi(1,-1,-2)=4(-1)(-2)^{3}+3(1)(-1)(-2)-(-2)^{2}+2$$ $$\phi(0,-3,1)=4(-3)(1)^{3}+3(0)(-3)(1)-(1)^{2}+2$$ and $$\phi(1,2,3)=4(2)(3)^{3}+3(1)(2)(3)-(3)^{2}+2$$ Can you continue from here?