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

Ask an Expert

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

Write your message here..

Related Questions

Union and intersection - set theory, Union and Intersection - Set theory ... 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

Asymtotes, vwertical and horizontal vwertical and horizontal

Prove asymptotic bounds for recursion relations, 1. (‡) Prove asymptotic b... 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

Homogeneous differential equation, Assume that Y 1 (t) and Y 2 (t) are two ... Assume that Y 1 (t) and Y 2 (t) are two solutions to (1) and y 1 (t) and y 2 (t) are a fundamental set of solutions to the associated homogeneous differential equation (2) so, Y

Equation of a straight line, In a two dimensional case, the form of t... In a two dimensional case, the form of the linear function can be obtained if we know the co-ordinates of two points on the straight line. Suppose  x' and  x"  are two

Math, could you help me get bater at math could you help me get bater at math

Sketch the exponental graph of f( x )=2x and g( x )= 1/2 , Example Sketc... Example Sketch the graph of following f( x ) = 2x  and  g( x ) = ( 1 /2) x Solution Let's firstly make a table of values for these two functions. Following is

Find the 14th term in the arithmetic sequence. 60, Find the 14th term in t... Find the 14th term in the arithmetic sequence. 60, 68, 76, 84, 92

Pre-algebra, How do you solve a table to get the function rule? How do you solve a table to get the function rule?

Error in measurement, what is actual error and how do you find percentage e... what is actual error and how do you find percentage error