Question

Can anyone help with an assignment on Basic Rules of Differentiation / Marginal Analysis?

Answer 1

2)
\[g(x)=y=x^x\]
\[\ln y=\ln x^x\]

Answer 2

\[\ln y=x \ln x\]
\[\frac1y y'=1 \ln x+x \frac1x\]
\[y'=y(\ln x+1)\]
\[y'=x^x(\ln x+1)\]

Answer 3

Is there another way of figuring this out without using ln? We haven't done that in any assignments yet.

Answer 4

\[y'=g'(x)=x^x (\ln x+1)\]
\[g'(2)=2^2(\ln2+1)\]
\[g'(2)\approx6.77\]

Answer 5

3)
f(x)=ax^2+bx+c
f(6)=150
f(10)=50

Answer 6

f(8)=100

Answer 7

150=36a+6b+c
50=100a+10b+c
100=64a+8b+c