Purchase Solution

L'Hospital's Rule, Asymptotes, Global Extrema, Inflection Points and Concavity : f(x) = x^2 e^(17x)

Not what you're looking for?

Ask Custom Question

F(x) = x^2 e^(17x)

1. Find an equation for each horizontal asymptote to the graph of f.
2. Find an equation for each vertical asymptote to the graph of f.
3. Determine all critical numbers.
4. Determine the global maximum of the function.
5. Determine the global minimum of the function.
6. Find inflection points.
7. Find intervals of concave downward.
8. Give a rough sketch of your graph

Purchase this Solution

Solution Summary

L'Hospital's Rule, Asymptotes, Global Extrema, Inflection Points and Concavity are investigated for f(x) = x^2 e^(17x). The solution is detailed and well presented.

Solution Preview

Hi, here is the solution,

f(x)= x^2 e^17x.

(i) Horizontal asymptote:

There are no asymptotes, because the curve is a simple polynomial.

Note: For simple polynomial asymptotes does not exist.

Critical point:

To find the critical point, we have to find the derivative and equate to zero, then find the values for x.

f(x) = x^2. e^17x

f '(x) = 2x. e^17x +17 x^2. e^17x

f'(x) = xe^17x( 2+ 17x)

Now, make f '(x)=0

so, x e^17x (2+17x) =0

2+17x = 0

17x = ...

Purchase this Solution

Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.