# calculus

Find the extreme values of the function for the given intervals.

2x^3 – 21x^2 + 72x

a) [0,5]

b) [0,4]

I have both the minimum values for both intervals which is 0. But I am unable to find the maximum. please help!!!

1. 👍 0
2. 👎 0
3. 👁 184
1. You have probably found two extrema where f'(x)=0.
To identify whether the extremum is a maximum or minimum, use the second derivative test.
If the second derivative is positive, the extremum is a minimum. If the second derivative is negative, the extremum is a maximum.

Here the extrema are at x=3 and x=4.

The second derivative, f"(x)=12x-42,
so for example, f2(3)=-6, so x=3 is a maximum.

Use your calculator to plot the graph of the function to help you solve these problems. After some time, you will be able to visualize the graph from the equation, even without the calculator.

1. 👍 0
2. 👎 0
2. I tried 3 for both (a and b) as a maximum and didn't work....

1. 👍 0
2. 👎 0
3. It is important to know that extreme values include local maxima, local minima and end-points of the given interval.

The question requires the extreme values of the function, so it is the value of the function that counts.

To find extreme values, we calculate the critical points (where f'(0)=0 and where f'(0) does not exist) as well as the value of the function at end-points.

Given
f(x)=2x^3 – 21x^2 + 72x

1. We calculate the points where f'(x)=0, and we have determined that f(3)=81 is a local maximum and f(4)=80 is a local minimum.

2. For [0,4], the values of the function at end-points are:
f(0)=zero, and f(4)=80.
So the list of values to consider are:
(0,zero)
(3,81)
(4,80)
We conclude that the extreme minimum is zero, and the extreme maximum is 81.

3. For [0,5], the values of the function at end-points are f(0)=zero, and f(5)=85.
So the list of values to consider for extreme values are:
(0,zero)
(3,81)
(4,80)
(5,85)
We choose zero as the extreme minimum, and 85 as the extreme maximum.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### calculus

2. Consider the function f defined by f(x)=(e^X)cosx with domain[0,2pie] . a. Find the absolute maximum and minimum values of f(x) b. Find the intervals on which f is increasing. c. Find the x-coordinate of each point of

2. ### trigonometry

find the exact values of s in the given intervals that have the given circular function values. 1. [pi/2,pi]; sin s=square root 2/2 2. [pi/2,pi]; cos s=-square root 3/2

3. ### Algebra

Complete the table for each function. 1. f(x) = √x The x values are 0, 1,4 and 9. The corresponding y values that I got are 0, 1, 2 and 3. 2. g(x) = -1/4√ x The x values are 0, 1, 4, and 9. The corresponding y values that I

4. ### calculus

Find the break-even point for the firm whose cost function C and revenue function R are given. C(x) = 16x + 10,000; R(x) = 21x

1. ### Calculus - Functions?

#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of

2. ### Calculus

The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Right Rectangle Approximation, using the 4 intervals between those given

3. ### Calculus

The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Sum Approximation, using the intervals between those given points.

4. ### Calculus

1. The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given

1. ### Calculus

Consider the function of defined by f(x)=x^3/3-4/x a. Find the X values for the points of inflection. b. Determine the intervals where the function of f is concave up and concave down.

2. ### Calculus help

The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Right Hand Sum Approximation, using the intervals between those given points.

3. ### Calculus Finals Review sheet!! Explanation needed

Here is a graph of the derivative y' of a continuous, differentiable function. For approximately what values of x between Ã¢Ë†â€™5 and 5 does the original function y have inflection points? Find limit as x approaches 3.5

4. ### Calculus

Consider the function f(x)=ln(x)/x^6. For this function there are two important intervals: (A,B] and [B,∞) where A and B are critical numbers or numbers where the function is undefined. Find A Find B For each of the following