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Find the point on the curve $y=x^{3}$ at which the tangent line at (2,8) crosses the curve. (You may want to use the result of Exercise $17 .$ )

(-4,-64) and (2,8)

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 1

Slope of a Curve

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.

04:05

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06:24

03:54

First we find the tangent line of the function y equals s cubed at a .28. The directive of the function as three X squared And the valuable derivative at two as trump. So the tangent night is Y -8 equals the slope of the Tangent. v. 12 times X miners too. And if we simplify this aquarium, we get why echoes 12 x minors 16. This is the quitting of 10.9. And next we calculate the crossing point. That is we just let X squared. He calls 12 eggs when you're 16 and remove the right hand side to the left hand side, which gives X square minors 12. Yaks. Last 16 until zero. We can solve the secret in which gives us X equals four. And the function value at four. Sorry. Mexico's miners for. And the function value at -4 is miners 60. Sure enhance The Crossing Point is -4 -64.

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