Perform a first derivative test on the function f(x) = - 5x2 – 3x + 4; [- 4,4]. a. Locate the critical points of the given function. b. Use the first derivative test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). a. Locate the criticai points of the given tunction. Select the correct cnoice below ana, It necessary, TIli in the answer box to compiete your cnoice. O A. The critical point(s) is/are at x = 3 10 (Simplify your answer. Use comma to separate answers as needed.) O B. The function does not have a critical point. b. Locate the maximum value. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. 3 There is a local maximum at x = 10 (Simplify your answer.) O B. There is no local maximum. Locate the minimum value. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. There is a local minimum at x = (Simplify your answer.) O B. There is no local minimum. c. Identify the absolute maximum value of the function. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. 89 The absolute maximum value is 20 (Simplify your answer.)
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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![Perform a first derivative test on the function f(x) = - 5x2 – 3x + 4; [- 4,4].
a. Locate the critical points of the given function.
b. Use the first derivative test to locate the local maximum and minimum values.
c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist).
a. Locate the critical points of the given function. Select the correct choice below and, if necessary, filI in the answer box to compiete your cnoice.
A.
3
The critical point(s) is/are at x =
10
(Simplify your answer. Use a comma to separate answers as needed.)
B. The function does not have a critical point.
b. Locate the maximum value. Select the correct choice below and, if necessary, fill in the answer box within your choice.
A.
3
There is a local maximum at x =
10
(Simplify your answer.)
B. There is no local maximum.
Locate the minimum value. Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. There is a local minimum at x =
(Simplify your answer.)
B. There is no local minimum.
c. Identify the absolute maximum value of the function. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A.
89
The absolute maximum value is
20
(Simplify your answer.)
B. There is no absolute maximum.
Identify the absolute minimum value of the function. Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The absolute minimum value is
(Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11bf6cf9-ca49-4055-b47e-2236fa624f2f%2Fb748cab9-a299-40f4-97f4-8a9ad021f51c%2F0e9ryrt_processed.png&w=3840&q=75)
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