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Find the equation of the tangent line to the graph of the given function at the given value of x. f(x)=x√√x +3; x = 1

Find the equation of the tangent line to the graph of the given function at the given value of x. f(x)=x√√x +3; x = 1

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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Question
**Question:** Find the equation of the tangent line to the graph of the given function at the given value of \( x \). \( f(x) = x^3 \sqrt[3]{x^3} + 3 \) ; \( x = 1 \) --- **Answer Choices:** - **A.** \( y = \frac{35}{6} x + \frac{20}{3} \) - **B.** \( y = \frac{35}{6} x - \frac{20}{3} \) - **C.** \( y = \frac{27}{4} x - \frac{19}{4} \) - **D.** \( y = \frac{27}{4} x - \frac{13}{4} \) --- **Note:** No graphs or diagrams are included within this question. The task involves finding the tangent line equation, which requires using derivatives and evaluating at the specific \( x \) value provided.
Transcribed Image Text:**Question:** Find the equation of the tangent line to the graph of the given function at the given value of \( x \). \( f(x) = x^3 \sqrt[3]{x^3} + 3 \) ; \( x = 1 \) --- **Answer Choices:** - **A.** \( y = \frac{35}{6} x + \frac{20}{3} \) - **B.** \( y = \frac{35}{6} x - \frac{20}{3} \) - **C.** \( y = \frac{27}{4} x - \frac{19}{4} \) - **D.** \( y = \frac{27}{4} x - \frac{13}{4} \) --- **Note:** No graphs or diagrams are included within this question. The task involves finding the tangent line equation, which requires using derivatives and evaluating at the specific \( x \) value provided.
Expert Solution
Step 1: We are using the derivative to find the tangent equation

f(x)=x3x3+3;x=1

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