How do you find the equation of the line tangent to the graph of #y=x^2# at x=2?
I found:
First you need the slope Graphically:
so
now you can use the relationship:
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To find the equation of the line tangent to the graph of y=x^2 at x=2, we can use the concept of differentiation.
First, we need to find the derivative of the function y=x^2 with respect to x. The derivative of x^2 is 2x.
Next, substitute x=2 into the derivative to find the slope of the tangent line at x=2. When x=2, the slope is 2(2) = 4.
Now, we have the slope of the tangent line, which is 4. To find the equation of the line, we also need a point on the line. Since the line is tangent to the graph of y=x^2 at x=2, we can use this point as our reference.
At x=2, the corresponding y-value on the graph is y=2^2 = 4. So, the point (2, 4) lies on the tangent line.
Using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values we have:
4 = 4(2) + b
Simplifying, we get:
4 = 8 + b
Subtracting 8 from both sides, we find:
b = -4
Therefore, the equation of the line tangent to the graph of y=x^2 at x=2 is y = 4x - 4.
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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.
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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