Answer:
[tex]x=2.28688[/tex] which you can round or truncate as you need to.
Step-by-step explanation:
Firstly, we need to understand what this question is asking us to do. The slope of the line tangent to the graph of [tex]f(x)[/tex] at x is simply [tex]f'(x)[/tex] at x.
This means that all we are doing is finding when the derivative is equal to 2.
Here is our setup.
[tex]0.1x+e^{0.25x}=2[/tex]
This is not a problem equation that you will be able to solve by hand as it utilizes a method that is not taught until later. This means that it is acceptable to use a calculator to find the solution.
In this case, we have two options. Graph both [tex]f(x)=0.1x+e^{0.25x}[/tex] and [tex]y=2[/tex] and find their intersection, or graph [tex]f(x)=0.1x+e^{0.25x}-2[/tex] and find its zero.
Either way, you get [tex]x=2.28688[/tex], which you can round or truncate as you need to.
