Question

It’s AP Calc, any ideas? Due by 4 pm

Answer 1

`x=2.28688` which you can round or truncate as you need to.

Explanation:

Firstly, we need to understand what this question is asking us to do. The slope of the line tangent to the graph of
`f(x)` at x is simply
`f'(x)` at x.

This means that all we are doing is finding when the derivative is equal to 2.

Here is our setup.

`0.1x+e^(0.25x)=2`

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
`f(x)=0.1x+e^(0.25x)` and
`y=2` and find their intersection, or graph
`f(x)=0.1x+e^(0.25x)-2` and find its zero.

Either way, you get
`x=2.28688`, which you can round or truncate as you need to.