# Calculus

Find the largest and smallest values of the given function over the prescribed closed, bounded interval of:

f(x)=(3x-1)e^-x for 0<x<2

1. 👍 0
2. 👎 0
3. 👁 574
1. f(x)=(3x-1)e^-x
Calculate f'(x) to find local extrema:
f'(x)=-(3x-4)e^(-x)
e^(-x) can never be zero, therefore
(3x-4)=0, or
x=4/3, which is on the interval [0,2].
f"(4/3)=-0.79 (4/3 is a maximum)
Now calculate f(0) and f(2) and compare the three values
f(0),f(2) and f(4/3) to determine which are the maximum and minimum.

1. 👍 0
2. 👎 0
2. How did you get (3x-4) from (3x-1) when you took the first derivative?

1. 👍 0
2. 👎 0
posted by Carly
3. If we take
f(x)=(3x-1)e^(-x)
=u.v
where u=(3x-1), v=e^(-x)
then
f'(x)=u'v + v'u
=3e^(-x) -e^(-x)(3x-1)
=-e^(-x)[-3 + 3x -1]
=-e^(-x)(3x-4)

Are you OK with the rest?

1. 👍 0
2. 👎 0

## Similar Questions

1. ### math

Find the largest and smallest values of the given function over the prescribed closed, bounded interval. F(x)=e^{x^2-2x} for 0

asked by Anna Kirakosyan on November 3, 2016
2. ### Another Calculus

Sorry I have been trying to figure this out all day. Find the largest and smallest values of the given function over the prescribed closed, bounded interval. g(t)= (t^3/2)(e^-2t) for 0

asked by Carly on July 11, 2011
3. ### mathematics

find the smallest and largest values ​​of the function f(x)=(x+1)∛x² on the interval [-4/5;3]

asked by lisa on June 11, 2011
4. ### Chemistry

Which response presents ions in order of increasing atomic radius? a) smallest Cl-, K+, Na+ largest b) smallest Cl-, Na+, K+ largest c) smallest K+, Na+, Cl- largest d) smallest Na+, K+, Cl- largest I would assume the answer would

asked by Anonymous on May 7, 2017
5. ### Calculus Help!!

Region R is bounded by the functions f(x) = 2(x-4) + pi, g(x) = cos^-1(x/2 - 3), and the x axis. a. What is the area of the region R? b. Find the volume of the solid generated when region R is rotated about the x axis. c. Find all

asked by Anonymous on December 21, 2012
6. ### Calculus

1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2]. 2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[-4,-2]. If Rolle's Theorem can be

asked by Cynthia on October 30, 2012
7. ### Math

For homework we're supposed to give all the properties of different functions. I was able to do all of it except for this one greatest integer function - f(x) = -1/2 [x-1] These functions always mess me up! Could someone tell me

asked by Rosanna on September 19, 2006
8. ### Calculus

The function f(x)=(x^4)-(10x^3)+(18x^2)-8 is continuous on the closed interval (1,8). Find the absolute minimum and maximum values for the function on this interval. Please help me!!! And please show your work so that i

asked by Sam on March 17, 2011
9. ### Caluclus

[Mean Value Theorem] f(x)=-3x^3 - 4x^2 - 2x -3 on the closed interval [0,8]. Find the smallest value of c that satisfies the conclusion of the Mean Value Theorem for this function defined on the given interval. I got 8 -

asked by Z32 on October 23, 2009
10. ### Maths

Find the absolute maximum and minimum values of the function f (x) = [x^(2/3)]*[x − 1] on the closed interval [0, 4], and state where these values occur.

asked by Khyati on October 21, 2014

More Similar Questions