# How do I visualize derivatives? I know how to derive functions, but for some reason I need a visual to fully understand the concept.

See answer below

Given: How do I visualize derivatives?

Derivatives are slope functions. When you evaluate a derivative at any location along the original function, you get the slope at that location.

If the original function is a cubic (degree = 3), then it's first derivative is a quadratic (degree = 2) function. Wherever there was a relative maximum or relative minimum in the original function, the slope will be zero which means the first derivative's

This would be the degree of the derivatives is you have a cubic function as the original function:

1st derivative: quadratic

2nd derivative: linear function

3rd derivative: horizontal line

4th derivative: y = 0

Here's an example:

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Visualizing derivatives can help in understanding how the slope of a function changes at different points. One way to visualize derivatives is by looking at the tangent lines to a curve at various points. At any given point on the curve, the derivative represents the slope of the tangent line at that point. As you move along the curve, the slope of the tangent line changes, indicating how the function is changing.

Another way to visualize derivatives is by considering the graph of the derivative function itself. The derivative function shows how the slope of the original function changes with respect to the input variable. Areas where the derivative function is positive indicate that the original function is increasing, while areas where the derivative function is negative indicate that the original function is decreasing. Zero crossings of the derivative function correspond to points where the original function has local maxima or minima.

Overall, visualizing derivatives involves understanding how the slope of a function changes over its domain and interpreting this information geometrically on graphs or through tangent lines.

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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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