Find out function is increasing and decreasing, Mathematics

Assignment Help:

Find out where the following function is increasing & decreasing.

A (t ) = 27t 5 - 45t 4 -130t 3 + 150

Solution

As with the first problem first we need to take the derivative of the function.

A′ (t ) = 135t 4 -180t 3 - 390t 2  = 15t 2 (9t 2 -12t - 26)

Next, we have to determine where the function isn't changing.  It is at,

t = 0

1966_function is increasing.png

Thus, the function is not changing at three values of t.  At last, to find out where the function is increasing or decreasing we have to determine where the derivative is +ve or -ve.

Recall that if the derivative is +ve then the function have to be increasing & if the derivative is -ve then the function have to be decreasing. The given number line gives this information.

2423_function.png

Thus, from this number line we can illustrate which we have the given increasing & decreasing information.

Increasing : - ∞ < t < -1.159, 2.492 < t < ∞

Decreasing : -1.159 < t < 0, 0


Related Discussions:- Find out function is increasing and decreasing

Series solutions to differential equations, Before searching at series solu...

Before searching at series solutions to a differential equation we will initially require to do a cursory review of power series. So, a power series is a series in the form, .

Sequences - calculus, Sequences Let us start off this section along wi...

Sequences Let us start off this section along with a discussion of just what a sequence is. A sequence is nothing much more than a list of numbers written in a particular orde

How many people are usual to vote for mr salva on survey, The Daily News re...

The Daily News reported that 54% of people surveyed said in which they would vote for Larry Salva for mayor. Based on the survey results, if 23,500 people vote in the election, how

Probability distributions, Probability Distributions Since the value of...

Probability Distributions Since the value of a random variable cannot be predicted accurately, by convention, probabilities are assigned to all the likely values that the varia

Divide by 1-digit numbers, which experession can be used to check the quoti...

which experession can be used to check the quotient 646 divided by 3

Limit problem, limit x-a/|x-a| equals x-a [a]a [b]0 [c]-a [d]none 0f these

limit x-a/|x-a| equals x-a [a]a [b]0 [c]-a [d]none 0f these

Calculate the density of people per square mile, 1.  In 1900, a certain cou...

1.  In 1900, a certain country's population was 77,977,459 and it's area was 2,821,924 square miles, In 2000, the country's population was 283,575,229 and its area was 3,551,003 sq

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd