# What is Rate of Change of a Function?

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The rate of change of a function describes how the output value of the function changes in response to a change in the input value. It is calculated by finding the ratio of the change in output to the change in input over a specific interval. Mathematically, it can be expressed as the derivative of the function with respect to its input variable. The rate of change can indicate whether the function is increasing, decreasing, or remaining constant over that interval.

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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.

- What is the equation of the tangent line of #f(x)=sqrt(1/(x^2-3x+2) # at #x=0#?
- What is the equation of the line normal to # f(x)=1/(x^2-2) # at # x=1#?
- How do you find the equation of a line tangent to #y=x^2-2x# at (3,3)?
- How do you use the definition of a derivative to find the derivative of #f(x) = 4 + 9x - x^2#?
- How do you use the limit definition to find the derivative of #y=sqrt(-4x-2)#?

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