Question 91084
 I would skip evaluation part, that's tedious calculation.

for the second part, observe the following graphs

f(x)=3x+2 --- brown
f(x)=x^2+5x+6 -- green
f(x)=x^3+3x^2+2x+1 -- blue
f(x)=e^x --- purple
f(x)=logx --- close to x axis

from the slopes you can see the rate of change, the bigger the slope the bigger the rate of change.


{{{graph(300,600,-5,10,-10,80,3x+2,x^2+5x+6,x^3+3x^2+2x+1,2.71828^x, (ln(x))/ln(10))}}}

It is hard to tell which rate is bigger between the blue one and purple one, the following graph is the graphs of derivatives of  f(x)=x^3+3x^2+2x+1  and
f(x)=e^x , the green one is for f(x)=e^x, and green one eventually goes above f(x)=x^3+3x^2+2x+1, that means e^x has bigger rate of change than x^3+3x^2+2x+1 
after a certain value of x.
 

{{{graph(200,300, -2, 6, -5, 50, 3*x^2, 2.71828^x)}}}

the conclusion:

the increase rate is in the following order, from smallest to biggest

f(x)=logx  
f(x)=3x+2  
f(x)=x^2+5x+6  
f(x)=x^3+3x^2+2x+1 
f(x)=e^x  


hope this helps you and your daughter.