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If the tangent line to $ y = f(x) $ at $ (4, 3) $ passes through the point $ (0, 2) $, find $ f(4) $ and $ f'(4) $.

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$f(4)=3 ; f(4)=1 / 4$

02:06

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

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have a question in this. It has given that pendant line to wife will affect passes through the zero common tool. So if this is any curve Well I could have had opinions line And this is for from a three it is passing through 10 comma two. Yeah. Uh huh. We have to find a four and a flash for Okay so let's get started. Well we see that right This four common 3 point lies on this. Why would affect so this is the value of X and this is the value of X corresponds to a value of Y. Our value the function F X corresponds to responding to X equal to full. So we can say that Ben x equal to four. FFS Will be equal to three. So on the other hand on other way we can see that has four equal to three because this is in order to bear for equal to think and we need to find the value of dash for dash police slope of the tangent at this point the flow of attendant at this point will be slow will be the slope of this tendon and the flow of this land which is passing through two points for commentary and zero comma two so half dash four will be able to if this is excellent. This is excellent. Common by one. This is extra. Come away to the struggle. This line will be Y tu minus y one X two minus excellent. So three by two minus three -1 x -4. Given by four. Thank you

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