# How do you find the equation of the line tangent to #f(x)=2x^2# at x=-1?

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To find the equation of the line tangent to f(x)=2x^2 at x=-1, we need to find the slope of the tangent line and the point of tangency.

First, we find the derivative of f(x) with respect to x, which gives us f'(x)=4x.

Next, we substitute x=-1 into f'(x) to find the slope of the tangent line at x=-1. So, f'(-1)=4(-1)=-4.

Now, we have the slope of the tangent line, which is -4.

To find the point of tangency, we substitute x=-1 into f(x). So, f(-1)=2(-1)^2=2.

Therefore, the point of tangency is (-1, 2).

Finally, we can use the point-slope form of a linear equation, y-y1=m(x-x1), where m is the slope and (x1, y1) is a point on the line.

Substituting the values, we have y-2=-4(x-(-1)).

Simplifying the equation, we get y-2=-4(x+1).

Expanding further, we have y-2=-4x-4.

Rearranging the equation, we get y=-4x-2.

Thus, the equation of the line tangent to f(x)=2x^2 at x=-1 is y=-4x-2.

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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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