Simple differentiation problem

In summary, by differentiating the given functions, we can find their points of extremum. By equating the x-values of these points, we can determine that a=b. However, in order for the functions to share a point of extremum, the y-values must also be equal. Therefore, further analysis is needed to find the correct values of a and b.
  • #1
hancmarginis
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  • #2
hancmarginis said:
Find a and b such that the function e^x*(ax+b) shares a point of extremum with the function x^2*e^x .

So differentiating the latter and finding its p.o.e's gives x= -2 or x=0.

Differentiating the former and plugging x= -2 in, gives:
f'(x) = e^x*(a+ax+b) = 0 for p.o.e
f'(-2)= a-2a+b=0
so a=b.
Now what?

I know this question is insultingly easy, but I cannot see where I've gone wrong. It's disgusting.

You have equated the x-values, but not the y-values; sharing a point means having the same x and y both.
 

Related to Simple differentiation problem

1. What is differentiation?

Differentiation is a mathematical process of finding the rate of change of a function with respect to its independent variable. It helps us understand how a function's output changes when we make small changes to its input.

2. What is a simple differentiation problem?

A simple differentiation problem involves finding the derivative of a basic function, such as a linear or quadratic function, using the basic rules of differentiation.

3. What are the basic rules of differentiation?

The basic rules of differentiation include the power rule, product rule, quotient rule, and chain rule. These rules allow us to find the derivative of a function by manipulating its algebraic form.

4. Why is differentiation important in science?

Differentiation is important in science because it allows us to model and analyze the rate of change of physical quantities, such as velocity, acceleration, and growth rates. It is used in fields such as physics, chemistry, biology, and economics.

5. How can I improve my skills in solving simple differentiation problems?

To improve your skills in solving simple differentiation problems, it is important to practice regularly and familiarize yourself with the basic rules of differentiation. You can also seek out additional resources, such as textbooks or online tutorials, and work through practice problems to strengthen your understanding.

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