Question

It’s AP Calc, any ideas? Due by 4 pm

Answer 1

Answer:

$x=2.28688$ 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 $f(x)$ 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.