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20 Dec 2021
Problem 74
Page 183
Section: 3.1 Derivatives of Polynomials and Exponential Functions
Chapter 3: Differentiation Rules
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20 Dec 2021
Given information
We are given the parabolic equation and .
Step-by-step explanation
Step 1.
The parabola intersect the -axis at .
Notice that is a quadric formula with negative discriminant, therefore, it has no real solutions.
All points on the parabola has the form .
All points on the parabola has the form .
We know that the slope of a tangent at any point is the derivative at that point : .
Applying The Power Rule and The Constant Multiple Rule, we obtain :
Assume that there is a tangent that passes through those two points.
Hence, we required that derivative has common solution :
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