Answer:
1. Slope at a=2 is 2.
2. Slope at a=0 is 2.
Step-by-step explanation:
We need to find the slope of y = f(x) at x = a.
1.
The given function is
[tex]f(x)=x^2-2x[/tex]
It can be written as
[tex]y=x^2-2x[/tex]
Differentiate with respect to x.
[tex]y'=2x-2[/tex]
Substitute x=2 to find the slope of y = f(x) at a=2.
[tex]y'=2(2)-2[/tex]
[tex]y'=4-2[/tex]
[tex]y'=2[/tex]
Therefore the slope of function at a=2 is 2.
2.
The given function is
[tex]f(x)=\sin 2x[/tex]
It can be written as
[tex]y=\sin 2x[/tex]
Differentiate with respect to x.
[tex]y'=2\cos 2x[/tex]
Substitute x=0 to find the slope of y = f(x) at a=0.
[tex]y'=2\cos 2(0)[/tex]
[tex]y'=2(1)[/tex]
[tex]y'=2[/tex]
Therefore the slope of function at a=0 is 2.
