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At what point on the curve $ y = 1 + 2e^x - 3x $ is the tangent line parallel to the line $ 3x - y = 5? $ Illustrate with a sketch.

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01:06

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Harvey Mudd College

Baylor University

Idaho State University

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.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Hey, it's Claire. So when you married here have to note that parallel lines have equal slope. So we have three X minus y this equal to five. This becomes why is equal to three X minus five. So the slope is three. You have. Why is equal to one plus two e to the X minus three X. We're gonna differentiate. We get to eat the X minus three we have to solve. When this is equal to three. So X becomes equal to Ln of three. Access equal to Ellen of three. You have why is equal to one plus two e the L one of three minus three l one of three just equal to seven minus three. Ellen three. So there's a tension that l and three comma seven minus three Ellen of three. So the equation of the tangent becomes set. Why minus seven minus three. Ellen of three over X minus Ellen of three. Equal three. And why becomes equal to three X minus six? Well, end of three plus seven. We're going to make a sketch says why x So we have why, for one plus two. Eat the X minus three x Well, look, something like this. Then we have our tangent in red and then three x minus y equals five for our blue are green.

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