Answer:
y = -2x + 3
Step-by-step explanation:
The given equation is:
[tex]f(x)=x^2-2x+3[/tex]
First we need to find the slope of the tangent line. This can be done by finding the derivative of the given function.
[tex]f'(x)=2x-2[/tex]
Slope of the tangent will be the value of the derivative at the given point. So the slope of tangent is:
[tex]f'(0)=2(0)-2=-2[/tex]
Now we have slope of the tangent line and a point (0, 3) on the tangent. The point (0,3) is the y-intercept of the tangent line. So we can use slope-intercept form to directly write the equation of the line.
The slope intercept form of an equation is:
y = mx + c
where m is the slope and c is the y-intercept.
Using the values: m = -2 and c = 3, we get:
y = -2x + 3
This equation represents the tangent line
