# Thread: Understanding A Function using its derivative?

1. ## Understanding A Function using its derivative?

A test question states that f'(x)$\displaystyle \leqslant$ 5 for all values of x, and that f(0) = -3. What is the maximum possible value for f(4)?

What in god's name do I do? I understand that it means that the slope of f is never bigger than 5 but that's it. It has to do with applying mean value thereom

2. Originally Posted by RezMan

A test question states that f'(x)$\displaystyle \leqslant$ 5 for all values of x, and that f(0) = -3. What is the maximum possible value for f(4)?

What in god's name do I do? I understand that it means that the slope of f is never bigger than 5 but that's it.
1. Consider a straight line passing through (0, -3) with a slope of m = 5. It's equation is:
$\displaystyle y = 5x-3$

2. According to the text of the question the graph of f is always below this line or is this line. So the utmost value of f at x = 4 is: 5*4 - 3 = 17

3. oh my god you're right! I found to do it this way: 5$\displaystyle \geqslant \frac{f(4)+3}{4-0}$
20$\displaystyle \geqslant$ f(4)+3
17$\displaystyle \geqslant$ f(4)

thank you so much. Since this was a silly little problem should I remove it from the board?