# How do you determine the slope of a tangent line? Why does this work?

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To determine the slope of a tangent line, you can use the derivative of the function at the point of tangency. The derivative represents the rate of change of the function at any given point. By evaluating the derivative at the point of tangency, you can find the slope of the tangent line. This works because the derivative measures the instantaneous rate of change of the function, which is precisely what the slope of the tangent line represents.

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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 average rate of change of # f(x) = x^2+x+3# from [1,x]?
- How do you use the definition of a derivative to find the derivative of #f(x) = -7x^2 + 4x#?
- What is the equation of the normal line of #f(x)=x^3/sqrt(16x^2-x)# at #x=2#?
- How do you find the equation of the line tangent to #y=sin(2x)# at x=pi/2?
- What is the equation of the tangent line of #f(x) =sqrt(ln(sinx))# at # x = pi/4#?

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