# What is the equation of the line tangent to #f(x)=(x-3)^2-x # at #x=-1#?

In order to find the equation of the tangent line, we must first find the gradient of this line at the given point.

To do this we find the derivative of

We can expand this and then we only need to use the power rule to differentiate it.

Plug in

This is our gradient

We need the corresponding

Using point slope form of a line:

GRAPH:

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The equation of the line tangent to f(x)=(x-3)^2-x at x=-1 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.

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- How do you find the equation of the tangent line to the curve #f(x)= x + cos (x)# at x = 0?
- What is the equation of the tangent line of #f(x)=cos^3x/x^2 # at #x=pi/3#?
- What is the equation of the tangent to the line #sf(y=ln(x^2-8)# at the point (3,0) ?

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