4. Contextual Applications of Differentiation

Approximating Values Of A Function Using Local Linearity And Linearization — Quiz

Test your understanding of approximating values of a function using local linearity and linearization with 5 practice questions.

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Practice Questions

Question 1

A differentiable function $f$ is linearized at $x=2$ using $L(x)=f(2)+f'(2)(x-2)$. If $f(2)=5$ and $f'(2)=3$, what is the linearization $L(x)$?

Question 2

A function has $f(4)=10$ and $f'(4)=-2$. Using local linearity, what is the approximate value of $f(4.1)$?

Question 3

The function $f$ is differentiable and $f(1)=7$, $f'(1)=4$. Which value is the best approximation for $f(0.95)$?

Question 4

A student uses linearization at $x=3$ to approximate a function value. Which statement best describes why this method works well when $x$ is close to $3$?

Question 5

Let $L(x)$ be the linearization of a differentiable function $f$ at $x=a$. Which formula is correct?