find the point on the graph of y=x^2 where the tangent line is parallel to the line 2x-y=2
Y = X^2. 2X - Y = 2.
m = -A/B = -2 / -1 = 2 = Slope.
m2 = Y' = 2X = Slope of parabola.
Y' = 2X = 2,
2X = 2,
X = 1.
Y = X^2
Y = 1^2 = 1.
P(1, 1).
If you graph the parabola, you can use
the following points:
(-2,4), (-1,1), V(0,0), (1,1),(2,4).
To find the point on the graph where the tangent line is parallel to the line 2x - y = 2, we need to find the slope of the given line first.
Rearranging the equation 2x - y = 2, we get:
-y = -2x + 2
Simplifying further:
y = 2x - 2
The slope of the line 2x - y = 2 is 2.
Since the tangent line to the graph of y = x^2 at any point (x, y) has a slope of 2x, we need to find the x-coordinate where 2x = 2.
Solving 2x = 2 for x:
2x = 2
x = 1
Therefore, the point on the graph of y = x^2 where the tangent line is parallel to the line 2x - y = 2 is (1, 1).
To find the point on the graph of y = x^2 where the tangent line is parallel to the line 2x - y = 2, we need to first calculate the derivative of y = x^2 to find the slope of the tangent line.
Step 1: Calculating the Derivative
The derivative of y with respect to x, denoted as dy/dx or y', represents the slope of the tangent line at any point on the curve.
Taking the derivative of y = x^2 using the power rule, we get:
dy/dx = 2x
Step 2: Finding the Slope of the Given Line
The given line equation is 2x - y = 2. We can rewrite this equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Rearranging the equation, we get:
y = 2x - 2
Comparing this equation with the slope-intercept form, we see that its slope is 2.
Step 3: Finding the Point of Intersection
Since the tangent line is parallel to the given line, its slope should also be 2. Therefore, we need to find the point of intersection between the graph of y = x^2 and the line with slope 2.
Setting the derivative (slope of the curve) equal to the slope of the line, we have:
2x = 2
Solving for x, we find x = 1.
Substituting x = 1 back into the original equation, y = x^2, we get:
y = 1^2
y = 1
Therefore, the point on the graph of y = x^2 where the tangent line is parallel to the line 2x - y = 2 is (1, 1).