2. Differentiation(COLON) Definition and Fundamental Properties

Estimating Derivatives Of A Function At A Point — Quiz

Test your understanding of estimating derivatives of a function at a point with 5 practice questions.

Practice Questions

Question 1

What is the best estimate of the derivative of $f$ at $x=2$ if the secant slopes near $x=2$ are $3.8$ from the left and $4.2$ from the right?

Question 2

A graph of $f$ has a tangent line at $x=a$ with slope $-5$. What is the estimated value of $f'(a)$?

Question 3

Which statement best describes how to estimate $f'(3)$ from a table of values?

Question 4

Suppose $f(1.9)=7.6$ and $f(2.1)=8.4$. What is a good estimate of $f'(2)$?

Question 5

If a function is decreasing at $x=5$, which estimated derivative value is most reasonable?