Answered: Suppose that f is continuous at (4, 6)…

Suppose that f is continuous at (4, 6) and that f(4, y) = y' for y + 6. What is the value f(4, 6)? (Give your answer as a whole or exact number.) S(4, 6) =

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.2: Polynomial Functions

Problem 96E: What is the purpose of the Intermediate Value Theorem?

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Question

Suppose that f is continuous at (4, 6) and that f(4, y) = y for y + 6. What is the value f(4, 6)?
(Give your answer as a whole or exact number.)
f(4, 6) =

Expert Solution

Step 1

Given that $f$ is continuous at $(4, 6)$ and that $f (4, y) = y^{3}$ for $y \neq 6$ .

We have to find the value $f (4, 6)$ .

Since, given $f$ is continuous at $(4, 6)$ such that $f (4, y) = y^{3}$

Hence,

$\begin{matrix} f (4, 6^{-}) = {(6^{-})}^{3} \\ = 216 \end{matrix}$

Hence, $f (4, 6^{-}) = 216$

Here, $6^{-}$ is very small difference with $6$ for example $5.999999999 . . . . .$

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