# How do you find the equation of the line tangent to #f(x)=3/x^2# at x=2?

Next, we need to find the slope of the tangent line. This is the definition of the derivative, which gives the slope of the tangent line at a given point.

To differentiate the function, we will first need to write the function:

So, with the given information, this becomes:

Simplified, this becomes:

graph{(y-3/x^2)(y+3/4x-9/4)=0 [-3.8, 7.296, -1.983, 3.564]}

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To find the equation of the line tangent to the function f(x) = 3/x^2 at x = 2, we need to find the derivative of the function and evaluate it at x = 2.

First, let's find the derivative of f(x) = 3/x^2 using the power rule for differentiation.

f'(x) = -6/x^3

Next, we substitute x = 2 into the derivative to find the slope of the tangent line at x = 2.

f'(2) = -6/2^3 = -6/8 = -3/4

So, the slope of the tangent line at x = 2 is -3/4.

Now, we can use the point-slope form of a linear equation to find the equation of the tangent line.

y - y1 = m(x - x1)

Substituting the values, we have:

y - f(2) = (-3/4)(x - 2)

Simplifying further:

y - 3/(2^2) = (-3/4)(x - 2)

y - 3/4 = (-3/4)(x - 2)

y - 3/4 = -3/4x + 3/2

y = -3/4x + 3/2 + 3/4

y = -3/4x + 9/4

Therefore, the equation of the line tangent to f(x) = 3/x^2 at x = 2 is y = -3/4x + 9/4.

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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.

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