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Given $f(x)=\sqrt{x}(\text { a) }$ At which point will the tangent line be vertical? (b) What can you say about the derivative at this point?

(a) (0,0)(b) does not exist

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 1

Slope of a Curve

Derivatives

Campbell University

Baylor University

University of Nottingham

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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So we had a function have five x exploded, Great of X. The question is, at what point? Attention to this function is vertical, so prime a big is one over to a spirit of eggs. Okay, because this is equal to X to the over one half on. If you take the derivative of that, you would get this and so appointed X equal to zero. The tangent line. He's about to come on. What does it mean for derivative that mean derivative doesn't exist? It doesn't exist because at points into dysfunction is not defined that point.

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