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Question: Dutch book on Applied Math, part 2

Question: Dutch book on Applied Math, part 2

The function 110 Maple 2019
complex rootfinding plotting
September 17 2021
1

I have some more questions, now i get some more odd situations where an obvious answer cannot be given by solve. And a funtion cannot be plotted somehow. 

Here is the file. I tried to understand why, but it is not happening. They did it on purpose (i guess) to get simple questions, and show you that Maple sometimes does not have the answer right away. So you run into the "limitations" of the program right away so you are aware what could go wrong.

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Find x with the help of a graph from: 2^x<1/2*x^2+2  
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smartplot([2^x, (1/2)*x^2+2])

 
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solve(2^x = (1/2)*x^2+2, x)

Warning, solutions may have been lost

  

RootOf(_Z^2-2*2^_Z+4)

 (1)
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"f(x):=2^(x)"

proc (x) options operator, arrow, function_assign; 2^x end proc

 (2)
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"g(x):=1/(2)x^(2)+2"

proc (x) options operator, arrow, function_assign; (1/2)*x^2+2 end proc

 (3)
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evalf(solve(f(x) = g(x), x))

Warning, solutions may have been lost

  

.8841764608-2.067784075*I

 (4)
> 

While the answer is obviously x=2 to be equal, and thus for values of x= (infinity;2> g(x) is larger, even if you would manually fill in the equetions,you get a value of 2. Both sides would get a solution of y=4. Somehow Maple does not give a straight answer.

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``
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2nd question
I have to plot this function, and it wont let me plot it..

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"f(x):=(-2)^(x)"

proc (x) options operator, arrow, function_assign; (-2)^x end proc

 (5)
> 

plot(proc (x) options operator, arrow, function_assign; (-2)^x end proc)

 
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I am not seeing a line, it is so odd.

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Download Applied_Math_Part_1_questions_part_two.mw

The function
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