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Use the appropriate rules to determine the derivative.$$f(x)=3 x^{3}-7 x+9, \text { find } f^{\prime}(-1)$$

$$2$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 2

Derivatives Rules 1

Derivatives

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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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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Yeah. So the main thing with this problem is understanding that what the directions are asking you to dio, which is f prime, means to find the derivative. And then negative one is saying plug in negative one for ethics. So as we start this problem, just rewrite the problem. Three X cubed minus seven X plus nine. Yeah, uh, basically, what it's saying is, okay, we'll start by finding the derivative so f prime of X. Well, I'm expecting that you know the rules by now that you bring the exploding in front three times three is nine. Then you subtract one from your exponents so it becomes X to the second power. A zoo. Look at the next one. The implied exposes one. If you bring that in front one time seven is seven. And if you want to think this is X to the zero power, that's fine, because X to the zero power is equal to one. You know, seven times one is just seven. And then they expect you to know that the derivative of a constant is zero. So now all you have to do is take this negative one and replace it for that X And the expectation is that you know that Negative one when you square, it's positive one. So we're just looking at nine minus seven, which gives me an answer of to and there you have it.

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