Find the open interval(s) where the following function is increasing, decreasing, or constant. Express your answer in interval notation. f(x) = -(x- 2)-4

Q: Find the intervals on which the function is increasing or decreasing. f(x) = 2x³-6x²2-48x + 12 List…

A: The given function is: fx=2x3-6x2-48x+12. To Find: The intervals on which the function is increasing…

Q: Find the x- and y-intercepts of the graph of the function f(x) = -4x+1| +8. Enter your answers as…

A: 1.The x-intercepts are the point where the graph intersects the x-axis.The value of the y-coordinate…

Q: Write an equation for the function f(x), which is represented by the following graph:

A: here y-intercept is (0,0) so choose the sine function which is in the form of  there is no vertical…

Q: Fill in each blank for the function f(x) = 3x - 6. solve for each   f(-4) f(4) f(-2) f(0)

A: Given function fx=3x-6.  We need to find following parts, f-4, f4, f-2, f0.

Q: Find the domain for each function and express using interval notation. I + xS^ = (x)f b. x2-25 V3x+2…

A: A detailed solution is given below.

Q: State the domain of the function. ƒ1x2 =19 - x223>2

A:

Q: Graph the function f(x) = x-1

A: f(x)=x-1 For x-intercept: f(x)=0 =>x-1=0 =>x=1 For y-intercept: x=0 f(0)=0-1 =>f(0)=-1

Q: Find the domain of the function f(x) = – 2x? – 5x 1 Use interval notation to express your answer.

A:

Q: Write the equation for the following function: 10 9. 8 7. 4 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 2 3 4 5…

A: we know that equation of a line using two points(x1,y1) and (x2,y2) is gievn…

Q: х + 40, where 4 b. The temperature (in degrees Fahrenheit) can be approximated by the function c(x)…

A: For a function, y=f(x) , x is the independent variable and y is the dependent variable . Consider…

Q: Evaluate each function for the given value. a.  h(x) = 7 - 3/2x; h(4) b.  f(x) = [1-5x]; f(9)

A: To evaluate the functions at the given values

Q: (a) y = (1-2x²)³ (b) h(t) = 2t+3) 3 6-t²

A:

Q: Determine the domain of the following function, and write your response in interval notation. Write…

A: the domain of the function are the points at which the the value of the function is real and defined…

Q: f(x) = −5x³ +1 x y -2 -1

A:

Q: Find the x-intercept and y-intercept of the following function y = -7x 16

A: Given: A function y=-7x-16. To Find: x-intercept and y-intercept.

Q: juan earns $7 per hour plus $20 per week making picture frames.  write a function g(x) for juan's…

A: Given: Earning per hour = $7 Extra earning per week = $20 To find: Total earning of Juan’s in a week…

Q: State the domain and range of the function shown.

A: Consider the provided function, fx=-25-x2 State the domain and range of the function shown. The…

Q: Evaluate the function. f(x) = -63x + 4, for f(-1) f(-1) =

A:

Q: A cashier earns $7 an hour. If x is the number of hours worked, which function represents the…

A: Earning of cashier per hour = $7Number of hours he worked = x hoursLet total amount earned = $y

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.