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Use the first and second derivatives to sketch the graph of the given equation. Also include the intercepts, whenever they are easily determined.$$4 y^{2}-x^{2}=16$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 3

Concavity and the Second Derivative

Derivatives

Campbell University

Harvey Mudd College

University of Nottingham

Boston College

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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Use the first and second d…

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Find the $x$ - and $y$ -in…

the following problem. We want to use the 1st and 2nd relatives to sketch the graph of the equation. Um So in this case, what we have is Let's sulfur. Why? 1st? So we're gonna um move the X squared over. So I have um four Y squared equals X squared plus 16. And then we're going to divide this by four. Don't take the square root of both sides. Um So now that we have this, we see our graph here as a hyper Bella and then we can also graph the negative form of this. That's the actual graph that was given to us. And with this we can use the 1st and 2nd derivative. This is F. Of X. And we see that at the time of actual look like this and F. Double crime of axe, the second derivative will look like this.

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