Answer:
[tex](\ln(5), 19-5\ln(5))[/tex]
Step-by-step explanation:
The line can be represented as y=5x-8, so the slope of the line is 5.
The derivative of the curve is:
[tex]\frac{d}{dx} [9+2e^x-5x]\\=\frac{d}{dx} [9]+\frac{d}{dx} [2e^x]-\frac{d}{dx} [5x]\\=2e^x-5\\[/tex]
We need to set that equal to 5 to find the x coordinate of our desired point
[tex]2e^x-5=5\\2e^x=10\\e^x=5\\x=\ln(5)[/tex]
Now, just plug in x in the curve to solve for y:
[tex]9+2e^{\ln(5) } -5\ln(5) = y\\9+10-5\ln(5)=y\\19-5\ln(5)=y[/tex]
