You can
put this solution on YOUR website! 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.
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.
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.
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