Question

If a function is increasing, then its derivative is:

• A. Negative
• B. Zero
• C. Positive
• D. Undefined

Hint:

Think of the derivative as the "speedometer" of the function's height. If the speed is positive, you are moving up!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The derivative $f'(x)$ represents the slope of the function. The sign of the slope tells us the behavior of the function (increasing or decreasing).
Step 2: Detailed Explanation:

• If $f'(x)>0$, the slope is "upward," meaning the function is increasing.
• If $f'(x)<0$, the slope is "downward," meaning the function is decreasing.
• If $f'(x) = 0$, the function is at a stationary point (like a peak or valley).

Step 3: Final Answer:
The correct option is (c).