The derivative is a measure of the rate of change of a function. It is a way of specifying how a function changes as its input changes. The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. The simplest case of a derivative is the difference quotient of a function. The concept of the derivative of a function is a central notion in calculus.

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Heather Z.

Oregon State University

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University of Michigan - Ann Arbor

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Idaho State University

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So in this example, we're being asked to determine whether the slope of each line is positive, negative zero or undefined. So know this in your directions. They're not actually asking you to find specifically what the slope is just is characteristic. So why don't we start with Line? A. So let's take a notice at what line A is doing. So remember, whenever you're reading, graphs always go from left to right. So this graph in line A is decreasing as we go from left to right because it's going downwards. So remember any line that decreases from left to right will always have a negative slope. So for line A, the slope will be negative. All right, now let's talk about lying. B. Well, take a look at this line. It's a horizontal line. And what do we know about the slope of any horizontal line? Well, it's always equal to zero because notice there is no vertical change. There's just a horizontal change. So remember the slope for any horizontal line will always be zero and lastly line. See? Well, I know this for line. See that the line increases as we go from left to right so because it's increasing, that means the slow will be positive. So remember the slope summary. When you're lying increases from left to right, you'll have a positive slope. When it decreases, the slope will be negative. The slope of every horizontal line is zero, and I know we all have one in this case. But if you did have a slow a line that was vertical, it's slope with the undefined.

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Heather Z.

Oregon State University