Problem 2: A student was given a function $f(x)$ and was asked to calculate $f'(1)$. They calculated the value of $f'(1)$ using the derivative rules and found that $f'(1) = 0$. The graph of $f(x)$ is given below. Why is the student's answer definitely wrong?
Added by Arthur G.
Close
Step 1
To find the derivative of a function, you must first find the slope of the line that represents the function at a particular Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 85 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A student is working with a complicated function f and has shown that the derivative of f is always positive. A minute later, the student also claims that f(x) = 2 when x = 1 and when x = π. Without checking the student's work, how can you be certain that it contains an error?
Andrew N.
(An Amusement) Given the problem of finding $y^{\prime}$ if $y=x^{x},$ student A did the following: Wrong 1 $y=x^{2}$ $$ \begin{aligned} y^{\prime} &=x \cdot x^{x-1} \cdot 1 \quad\left(\begin{array}{l} \text { misapplying the } \\ \text { Power Rule } \end{array}\right) \\ &=x^{x} \end{aligned} $$ Student B did this: Wrong 2 $\begin{aligned} y &=x^{x} \\ y^{\prime} &=x^{x} \cdot \ln x \cdot 1 \\ &=x^{x} \ln x \end{aligned} \quad\left(\begin{array}{l}\text { misapplying the } \\ \text { Exponential } \\ \text { Function Rule }\end{array}\right)$ The sum $\left.x^{x}+x^{x} \ln x \text { is correct (Example } 5\right),$ so WRONG 1 + WRONG 2 = RIGHT Show that the same procedure yields a correct answer for finding the derivative of $y=f(x)^{g(x)}$
Transcendental Functions
General Exponential and Logarithmic Functions
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD