# How do you find the slope of a tangent line to the graph of the function #y^2-2x-4y-1=0#, at (-2,1)?

Slope of the tangent is

The first derivative of the function gives the slope of the line at any given point.

Given -

#y^2-2x-4y-1=0#

Differentiate implicitly

#2y dy/dx-2-4dy/dx=0#

#dy/dx(2y-4)=2#

#dy/dx=2/(2y-4)#

Slope at

#m=2/(2(1)-4)=2/(-2)=-1#

Slope of the curve at point

Slope of the tangent is

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To find the slope of a tangent line to the graph of a function, we need to find the derivative of the function and evaluate it at the given point.

First, let's rearrange the given equation to express y in terms of x: y^2 - 4y = 2x + 1 Completing the square, we get: (y - 2)^2 - 4 = 2x + 1 (y - 2)^2 = 2x + 5

Now, we can differentiate both sides of the equation with respect to x: 2(y - 2) * (dy/dx) = 2 Simplifying, we have: (y - 2) * (dy/dx) = 1 dy/dx = 1 / (y - 2)

To find the slope at the point (-2, 1), substitute the values into the derivative: dy/dx = 1 / (1 - 2) dy/dx = 1 / (-1) dy/dx = -1

Therefore, the slope of the tangent line to the graph of the function at (-2, 1) is -1.

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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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