Find the relative maximum and minimum fory=3x^2+30x+605.

Question

Question

Find the relative maximum and minimum fory=3x^2+30x+605. [4 marks]

math

Answer 1

Answer #1

y^{\prime}=6 x+30

Critical number(s)

$$ y^{\prime}=0=>6 x+30=0=>x=-5 $$

Critical number: -5

$$ y^{\prime \prime}=6>0 $$

$y(-5)=3(-5)^{2}+30(-5)+605=530$

By the Second DerivativeTest the function $y$ has the relative minimum with the value of 530 at $x=-5$.

The function $y$ has no relative maximum.

answered by: aex

Answer 2

Similar Homework Help Questions

Question 1 (25 Marks) a. Find the relative maximum and relative minimum points of the function,...

Question 1 (25 Marks) a. Find the relative maximum and relative minimum points of the function, f(x,y) -x2 ,3-12x + 12y-13 [S Marks] b. Evaluate the Laplace transform of the following functions: i. f(t)sin 5e2* [5 Marks] [5 Marks] [7 Marks] (t)-t2+ cos 3t a. Let f(t) = 8t5-5t2 + 5t + 1. Find L
2. Use the "method of corners" to find the maximum and minimum values, if they exist,...

2. Use the "method of corners" to find the maximum and minimum values, if they exist, of z 3x +2y subject to the constraints: 2y2 10 (16 marks) 3x+ y 2 10 x 2 0, y 2 0
Find the maximum and minimum of the objective function: F =3x+2y subject to constraints: x >...

Find the maximum and minimum of the objective function: F =3x+2y subject to constraints: x > 0 y > 0 x + 2y < 4 x - y<1 Maximum value = 8, at point (0,4) Minimum value =0, at point (0, 0) Maximum value = 8, at point (8/3, 0) Minimum value =0, at point (1, -3/2) Maximum value = 8, at point (2, 1) Minimum value =0, at point (-2/3, 1) Maximum value = 8, at point (2, 1)...

(1 point) Find the maximum and minimum values of the function f(x, y) = 3x² –...

(1 point) Find the maximum and minimum values of the function f(x, y) = 3x² – 18xy + 3y2 + 6 on the disk x2 + y2 < 16. Maximum = Minimum =
Find the absolute maximum and absolute minimum values of the function f(x, y) = 3x ^2...

Find the absolute maximum and absolute minimum values of the function f(x, y) = 3x ^2 + 2y ^2 on the unit disk x^ 2 + y ^2 ≤ 1 , as well as the (x, y) coordinates where these extrema occur.
Find the minimum and maximum values of z = 3x + 4y, if possible, for the...

Find the minimum and maximum values of z = 3x + 4y, if possible, for the following set of constraints. 5x + 8y 240 X+ 8y 2 16 x20, 720 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The minimum value is (Round to the nearest tenth as needed.) OB. There is no minimum value. Click to select and enter your answer(s) and Check Answer. 1 part remaining Clear...

Page 2 ame: Written Portion 1. [8 points) Find relative maximum and minimum values and stive...

Page 2 ame: Written Portion 1. [8 points) Find relative maximum and minimum values and stive maximum and minimum values and the the intervals the function is increasing and decreasing for f(x) = €28–322
Exercise nr. 1 Find the relative extrema (Specify if they are a minimum or maximum) and...

Exercise nr. 1 Find the relative extrema (Specify if they are a minimum or maximum) and the points of inflection if any. Make sure to write your answers as (x, y) bundles. a) f(x) = 2x(x – 4)3
Find the maximum and minimum values of the function f(x, y, z) = 3x - y - 3z

Find the maximum and minimum values of the function f(x, y, z) = 3x - y - 3z subject to the constraints x2 + 2z2 = 49 and x + y - z = -7. Maximum value is _______ , occuring at _______ , Minimum value is _______ , occuring at _______ .

Find the indicated maximum or minimum value of the objective function in the linear programming problem....

Find the indicated maximum or minimum value of the objective function in the linear programming problem. Maximize f - 30x + 40y subject to the following constraints. x + 2y = 48 x + y s 30 2x + y 50 x 20, y 20 Need Help? Read It Vatch It Talk to a Tutor -/12.5 POINTS HARMATHAP9 4.2.015.MI. EE Solve the following linear programming problem. Restrict x 20 and y 20. Maximize = 3x + 5y sub/ect to the...