# What is the equation of the line tangent to # f(x)=-x^2+4x-5/x+1# at # x=1 #?

Locate the point through which the tangent line will pass by using

When we differentiate term by term, we observe that the derivative of the function equals

which is also able to be written as

The function and its tangent line are graphed:

graph{[-2, 6, -11, 10]} = -x^2+4x-5x^-1+1-y)(y-7x+8)=0

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The equation of the line tangent to f(x)=-x^2+4x-5/x+1 at x=1 is y = -2x + 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.

- How do you find the slope of the tangent line for #f(x) = 3x^2# at (1,3)?
- What does it mean about a point if the tangent line has a slope of 0?
- What is the slope of the line normal to the tangent line of #f(x) = 2x-xsqrt(x-1) # at # x= 2 #?
- How do you find the equation of the line tangent to #y=sqrtx# at (1,1)?
- What is the equation of the line that is normal to #f(x)=2x^3-3x^2+5# at # x=1 #?

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