Differentiation Problem?

In summary, the conversation revolved around finding the absolute maximum and minimum values of a given function using the derivative. The correct solution was provided and the question regarding a factor in the final solution was clarified. It was also discussed that the absolute maximum/minimum can be found at a point where the derivative is 0 or at the endpoints of the given interval. The question of whether the equation x^2+2=0 has a real solution was also addressed.
  • #1
chaosblack
16
0
simple SIMPLE local extremia question

Homework Statement



Find the absolute maximum and absolute minimum values of f(x) = 3x^4 - 8x ^3 + 12x^2 -48x +25, where 0 <= x <= 3.


Homework Equations



N/a

The Attempt at a Solution



f'(x) = 12x^3 - 24x^2 + 24x -48
= 12 (x^3 - 2x^2 + 2x -4)
= 12 (x-2) (X^2 +2)

I know how to do the rest, but just wondering before I go on... What should i do with that one factor...do I omit the (x^2 +2)?
 
Last edited:
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  • #2
Well beside your first three lines of solution being irrelevant, it looks correct to me.

Edit: Actually you forgot a factor of 2 in your final h solution according to the symbolic result you derived earlier on.
 
  • #3
Okay thanks alot, I updated the thread with a different question lol
 
  • #4
Well you know that the absolute maximum/minimum lies at a place where the derivative is 0 or at the endpoints of the interval. Does x^2+2=0 have a real solution?
 
  • #5
haha...thanks man. I'm starting to forget to most simple stuff
 

What is differentiation?

Differentiation is a mathematical concept that involves finding the rate at which one variable changes with respect to another variable. It is used to calculate the slope of a curve or the rate of change of a function.

Why is differentiation important?

Differentiation is important because it allows us to understand how a function changes over time or in response to a change in another variable. It is used in many fields of science, including physics, chemistry, and economics.

What are the different methods of differentiation?

The most common methods of differentiation include the power rule, product rule, quotient rule, and chain rule. These rules allow us to differentiate different types of functions, such as polynomials, exponential functions, and trigonometric functions.

How is differentiation used in real-world applications?

Differentiation is used in a wide range of real-world applications, from predicting the trajectory of a projectile in physics to calculating the optimal production level in economics. It is also used in engineering to optimize designs and in biology to model population growth.

What are some common mistakes made when differentiating?

Some common mistakes made when differentiating include forgetting to apply the chain rule, incorrectly applying the power rule, and forgetting to use the product or quotient rule when necessary. It is important to carefully follow the rules and double-check your work to avoid these errors.

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