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Find a parabola with equation $ y = ax^2 + bx + c $ that has slope 4 at $ x = 1, $ slope -8 at $ x = -1, $ and passes through the point (2, 15).
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01:44
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 1
Derivatives of Polynomials and Exponential Functions
Derivatives
Differentiation
Missouri State 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.
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 clear. So when you read here, so we apply is people to a X square plus B X plus c We take the derivative and it becomes to a X plus be the slope is for for access equal to one in the slope is a at Xs equal to negative one. We're just going to solve thes We're gonna add these up and yet be as equal to negative too. We could use the first or second equation to find a and we got A is equal to three. After we plug in for B, we note that the problem passes through two comma 15 so to find See, we just plug in 15 for a to square plus B times two plus c and we just put in the A and B values that we caught when we get four times three plus two times negative too plus C and we got see if people to seven. So the parabola is why is equal to three X square minus two x plus seven
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