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
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...
icon
Related questions
Question
**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.
Expert Solution
Step 1

Calculus homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning