Find out all the critical points for the function, Mathematics

Assignment Help:

Find out all the critical points for the function.

1815_critical points.png

Solution

To determine the derivative it's probably simple to do a little simplification previous to we in fact differentiate.  Let's multiply root through the parenthesis & simplify as much as possible. It will let to ignore using the product rule while taking the derivative.

g (t ) = t (2/3) ( 2t -1) = 2t (5/3)  - t (2/3)

Now differentiate.

g′ (t ) =(10/3)t(2/3) -(2/3)t(-1/3) = 10t(2/3)/3 -(2/3t(1/3))

We will have to be careful with this problem.  While faced along a negative exponent it is frequently best to removes the minus sign in the exponent as we did above.  It isn't actually needed but it can make our life simple on occasion if we do that.

Notice that removal the negative exponent in the second term let us to correctly recognize why t = 0 is a critical point for this function.  Once we move second term to the denominator we can apparently see that the derivative doesn't exist at t = 0 and so this will be a critical point.  If you don't get rid of the -ve exponent in the second term several people will wrongly state that t = 0 is a critical point since the derivative is zero at t = 0 .  Whereas it may seem like a silly point, after all in each of case t = 0 is identified as a critical point, it is occasionally important to know why a point is a critical point.  Actually, in some sections we'll illustrates a fact that only works for critical points wherein the derivative is zero.

Thus, we've found one critical point (where the derivative doesn't present), however now we have to determine where the derivative is zero (provided it is certainly...). To help with this usually it's best to combine the two terms into a single rational expression.  Thus, getting a common denominator & combining gives us,

g′ (t ) =10t-2/3t(1/3)

Notice that still we have t = 0 as a critical point.  Doing this kind of combining has to never lose critical points; it's just being done to help us determine them.  As we can illustrate now it's become much easier to rapidly determine where the derivative will be zero.  Recall as well that a rational expression will just be zero if its numerator is zero

Thus, in this case we can illustrates that the numerator will be zero if t =(1/5) and hence there are two critical points for this function.

t = 0     and t = 1/5


Related Discussions:- Find out all the critical points for the function

Express the product of -9p3r and the quantity 2p - 3r, Express the product ...

Express the product of -9p3r and the quantity 2p - 3r in simplified form. The translated expression would be -9p3r(2p - 3r). Noticed that the key word product means multiply.

Fourier series - partial differential equations, Fourier series - Partial D...

Fourier series - Partial Differential Equations One more application of series arises in the study of Partial Differential Equations.  One of the more generally employed method

What is the area of the square in simplified form, If the side of a square ...

If the side of a square can be expressed as a2b 3 , what is the area of the square in simplified form? Since the formula for the area of a square is A = s 2 , then by substitut

Example of word problem, Example of Word problem: There is a man who i...

Example of Word problem: There is a man who is 21 years older than his son.  5 years ago he was four times as old as his son. How older are both now? Solution: Step 1

Systems of equations revisited, Systems of Equations Revisited We requ...

Systems of Equations Revisited We require doing a quick revisit of systems of equations. Let's establish with a general system of equations. a 11 x 1 + a 12 x 2 +......

Integers, students dont retain the topic, hoe to make it easier?

students dont retain the topic, hoe to make it easier?

Transition matrix for the probabilitiy, Suppose research on three major cel...

Suppose research on three major cell phones companies revealed the following transition matrix for the probability that a person with one cell phone carrier switches to another.

Function composition, Function composition: The next topic that we have to...

Function composition: The next topic that we have to discuss here is that of function composition. The composition of f(x) & g(x) is ( f o g ) ( x ) = f ( g ( x )) In other

Explain simplifying rational expressions, Explain Simplifying Rational Expr...

Explain Simplifying Rational Expressions ? A rational expression, or algebraic fraction, is an expression in which you have a polynomial divided by a polynomial. Sometimes it

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