Estimate f'(2) from table; where is f'(x) positive, negative?

[kernel6903]

Does anybody know how to solve this kind of math?

Suppose that f is given for x in the interval [0, 12] by:

x =	0	2	4	6	8	10	12
f (x) =	14	10	9	10	13	17	20

A. Estimate f '(2) using the values of f in the table.

B. For what values of x does f '(x) appear to be positive? (Give your answer as an interval or a list of intervals.)

C. For what values of x does f '(x) appear to be negative?(Give your answer as an interval or a list of intervals.)

 

[stapel]

Does anybody know how to solve this kind of math?

"This kind of math" is called "calculus".

Suppose that f is given for x in the interval [0, 12] by:

x =	0	2	4	6	8	10	12
f (x) =	14	10	9	10	13	17	20

A. Estimate f '(2) using the values of f in the table.

Since the derivative is the slope at the point, what estimate of the slope have you derived? (slope)

B. For what values of x does f '(x) appear to be positive? (Give your answer as an interval or a list of intervals.)

What does it mean, in terms of the graph (or of the y-values) of the function, for the derivative to be positive? On which intervals does the function appear to behave in that manner?

C. For what values of x does f '(x) appear to be negative?(Give your answer as an interval or a list of intervals.)

What does it mean, in terms of the graph (or of the y-values) of the function, for the derivative to be negative? On which intervals does the function appear to behave in that manner?

If you get stuck, please reply with a clear listing of all of your thoughts and efforts so far. Thank you!

 

[kernel6903]

"Calculus"

I am completely lost as how to solve this problem, that is why I posted it on the forum.