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tind E such that the line is tangant to the graph of the function. Line: 4ニ -Gx+3 function: guu)= C-x

tind E such that the line is tangant to the graph of the function. Line: 4ニ -Gx+3 function: guu)= C-x

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Text for Educational Website:** --- **Problem Statement:** Find the value of \( C \) such that the line is tangent to the graph of the function. **Given Line:** \[ y = -6x + 3 \] **Function:** \[ g(x) = C - x^2 \] --- **Explanation:** This problem involves finding the parameter \( C \) such that the linear equation becomes tangent to the quadratic function. A tangent line touches the curve at exactly one point, implying that they will have the same slope at that point and will meet once. Solving this involves setting the derivatives equal and checking if there is one point of intersection.
Transcribed Image Text:**Text for Educational Website:** --- **Problem Statement:** Find the value of \( C \) such that the line is tangent to the graph of the function. **Given Line:** \[ y = -6x + 3 \] **Function:** \[ g(x) = C - x^2 \] --- **Explanation:** This problem involves finding the parameter \( C \) such that the linear equation becomes tangent to the quadratic function. A tangent line touches the curve at exactly one point, implying that they will have the same slope at that point and will meet once. Solving this involves setting the derivatives equal and checking if there is one point of intersection.
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