Analyzing Functions

Question

Use the graph of f(x) below to estimate the value of f '(3):

Options:

1. -5
2. -1
3. 0
4. 1

Answer 1

f'(3) is the derivative of the function evaluated at x = 3. Or in other words, it is the slope of a line that is just barely touching the graph of the function, f(x) at x = 3... Also called the tangent line.

If you can imagine sketching a line that is barely skimming the graph above at x = 3, you should clearly see that this line has to have a negative slope. Looking at your choices, you could eliminate #3 and #4.

Also, you can see that the slope of this line would be a bit steeper than a slope = -1. The most reasonable answer is a slope of -5.

The answer is #1