# How do you find the point on the graph of #y = x^2# where the tangent line is parallel to the line #x + 2y = 4#?

The answer is:

Rather than trying to write down an explanation, I thought I would make a quick video to show you how it works.

Hope it helps :)

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To find the point on the graph of y = x^2 where the tangent line is parallel to the line x + 2y = 4, we need to determine the slope of the line x + 2y = 4.

First, we rearrange the equation x + 2y = 4 to solve for y: 2y = 4 - x y = (4 - x)/2 y = 2 - (1/2)x

The slope of this line is -1/2.

Next, we find the derivative of the function y = x^2 to determine the slope of the tangent line at any given point on the graph. dy/dx = 2x

To find the x-coordinate of the point where the tangent line is parallel to the line x + 2y = 4, we set the derivative equal to the slope of the line: 2x = -1/2

Solving for x: x = -1/4

Substituting this value of x back into the original equation y = x^2, we find the y-coordinate: y = (-1/4)^2 y = 1/16

Therefore, the point on the graph of y = x^2 where the tangent line is parallel to the line x + 2y = 4 is (-1/4, 1/16).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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