Some interpretations of the derivative, Mathematics

Some interpretations of the derivative

Example   Is f ( x ) = 2 x3 + 300 +4 increasing, decreasing or not changing at x = -2 ?

Solution:  We already know that the rate of change of a function is specified by the functions derivative so all we have to do is it rewrite the function (to deal along with the second term) and then take the derivative.

f ( x ) = 2 x3 + 300 x-3+4       ⇒       f ′ ( x ) = 6x2 - 900x-4  = 6x2 - 900/x4

Note as well that we rewrote the last term in the derivative back as fraction. It is not something we've done to this point & it is only being done here to help with the evaluation in the next step. It's frequently easier to do the evaluation with +ve exponents.

Hence, upon evaluating derivative we get

f ′ ( -2) = 6 ( 4) - 900/16 = - 129/4 = -32.25

Hence, at x = -2 the derivative is negative and therefore the function is decreasing at x = -2 .

 

Posted Date: 4/12/2013 2:40:18 AM | Location : United States







Related Discussions:- Some interpretations of the derivative, Assignment Help, Ask Question on Some interpretations of the derivative, Get Answer, Expert's Help, Some interpretations of the derivative Discussions

Write discussion on Some interpretations of the derivative
Your posts are moderated
Related Questions
Union and Intersection - Set theory B ∩ C indicates the intersection of B and C. it is the set having all those elements that belong to both B and C If B = {5, 8, 11, 20, 2


Array - when items are arranged in a regular rectangular pattern of rows and columns, counting how many there are. (e.g., if there are 3 rows of 5 girls each, how many girls are t

How should shoppers''stop develop its demand forecasts?

1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies. 1. C(n) = 3C(n/2) + n

You''ve decided you want a plant for your room. At the gardening store, there are 444 different kinds of plants (tulip, fern, cactus, and ficus) and 444 different kinds of pots to

Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers



Program of "surface of revolution" in MATLAB