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(a) Graph the function$ f(x) = x^4 - 3x^3 - 6x^2 + 7x + 30 $in the viewing rectangle [-3,5] by [-10,50].(b) Using the graph in part (a) to estimate slopes, make a rough sketch, by hand, of the graph of $ f' $. (c) Calculate $ f'(x) $ and use this expression, with graphing device, to graph $ f' $. Compare with your sketch in part (b).
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00:29
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 1
Derivatives of Polynomials and Exponential Functions
Derivatives
Differentiation
Oregon State University
Baylor University
University of Michigan - Ann Arbor
Lectures
04:40
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
44:57
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
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(a) Graph the function…
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(a) Use a graphing calcula…
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(a) Graph the function $g(…
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(a) Use a graphing device …
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Determine $f$ so that its …
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Determine an appropriate …
Hey, it's close when you read here. So for part A, I'll draw our graph, and it looks something like this for part B. We have All right, um, graph of our original and then we're gonna graph are derivative. I'll do it in green. So you have. And then you finally, for part C, we're going to find our We're gonna difference she our original function and we get this is equal to for X cubed minus nine X square minus 12 x my seven. And when we grab this, I look like this.
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