Find the domain of the function using interval notation. f(x) =    16 − 15x   Find the domain of the function using interval notation. f(x) =  1 x2 − x − 30

Q: f(x) = x - 6x + 9x – 6 For this function, on [-1,5] interval, the absolute maximum is 10 and the…

A:

Q: For the function f(x) = !!x2 + 3 find f -1(x)

A: the given function isf(x)=x2+3to find f-1(x)

Q: Find the y-intercept of the polynomial function. f(x) = x2(x - 1)(x - 6)

A: Find the y-intercept of the polynomial function.f(x) = x2(x - 1)(x - 6)

Q: Find (f- g)(x) when f(x) = 7x - 8 and g(x) = 2x - 2. O A. - 5x +6 О В. 5х-6 ОС. 9х -10 O D. 5x - 10

A: fx=7x-8gx=2x-2To find:f-gx

Q: Let f(x) = 2x - 5. g(x) = 4x - 1, h(x) = x2 + x + 2. Evaluate the function g(f[h(1)]) without…

A: We plug x=1 in h(x) first

Q: For a dosage of x cubic centimeters​ (cc) of a certain​ drug, the resulting blood pressure B is…

A:

Q: f(x) 49-x2 / x2-5x-36 and g(x) x2+11x+28/ x2-16x+63, find an equation of the given function.…

A:

Q: The absolute Extrema of the function f(x) = /-x²+ 8x - 15 on its domain are

A: Given,f(x)=-x2+8x-15

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

A: Given, the function g(x) = 3x3 – 9x, we have to check whether the function is concave upward or…

Q: Find the intercepts of the function. f(x) = (x + 4)(9x2 − 1)

A:

Q: 1. The function f(x) "2x2 + 10x models the height above the ground, in %3D cm, of a jumping frog…

A:

Q: At what value of x does the function f(x) = x^3 - 3x^2 - 9x change from increasing to decreasing

A: Increasing decreasing function problem

Q: Given the function f(x)=0.2(x−2)(x+1)(x−5), determine the end behavior of the function

A: Given the function,

Q: For the function f(x) = 3 (e - 8) + 2, find f(x).

A: Given f(x) and inverse of f(x)

Q: Find the zeros of the function f(x) = x² + 5x + 1 to the nearest hundredth

A:

Q: ch that the function X-4 x 5. f (x) =

A:

Q: Find the x- and y-intercepts for the function. x2 + 4x + 3 x2 + 11x + 28 f(x) x-intercept (x, y)…

A: Consider the function, fx=x2+4x+3x2+11x+28

Q: Q 2/ find the value of (k) to continue the function x3-3x2-4x+12 f(x)= x-3 * * x = 3

A:

Q: given the function h(x)=2/3-x, find f(1/2)

A: Note f=h. Given: h(x) = 2/3-x. So,       h(1/2)=2/3-(1/2)                =1/6

Q: For the functions 7 f (x) = h(x) = /(22)2 –- x² g(x) = 11 + 14x – x², - i) Find f(-2)= ii) find…

A:

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

A:

Q: 1 Find the domain of the function f(x) V4 - 2x – x²

A: fx=14-2x-x2

Q: -2x+6 Consider the function f (x) = x3+2x2-15x

A: Here we use basic definition of function.

Q: For the function f(x) = x² + 5x – 2, find (a) f(3) (c) -f(x) f(x + h) – f(x) (b) f(-x) (d) f(3x) (e)…

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

A: Plot the curve for g(x).

Q: find the value of (k) to continue the function x²-3x2-4x+12 f(x)={ * * 31 x-3 x = 3.

A:

Q: Find (f-1)'(a) for f(x) = *+1 2x + 3 2 when a = 5 (Enter an exact answer.)

A: Take f^-1(x)=y. Then find f^-1(x).

Q: For the function f(x) = 3x-2x-3x +2, find "(X). Then find f"(0) and "(4).

A:

Q: Find f'(x) for the function. 6x3 - 2x + 1 f(x) x2 "(x)

A: Given query is to find the derivative of the function.

Q: Find the inflection point, if it exists, of the function. (If an answer does not exist, enter DNE.)…

A:

Q: 8. For the function: f(x) = x² - 7x - 4 find f( - 5)

A:

Q: 2x+3 (1) Find the domain of the function_H(x)= 4r x -

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: For the function f(x)= x3 + ax2 + 2a2x + a, there exists a point of inflection at x = 2. Determine…

A:

Q: Find (f -1)'(a) for f(x) = 4x – 3 when a = –15. Enter an exact answer.

A: Our objective is to find an exact answer of the above question.

Q: f(x) = x3 -3x2 - 3x +1 x=-1 is a root of the function how would you show that?

A:

Q: find (f-g)x when f(x)=4-7x and g(x)=7x+1 a. (f-g)(x)=14x+5 b. (f-g)(x)=-14x+3 c.(f-g)(x)=-14x+5…

A:

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

A:

Q: 2 – 6x + 5 Find the domain of the function f(x) = x2 + 4x – 5

A: Domain: It is the set of values of x or independent variable for which the function is defined or…

Q: Find the upper and lower limits of the function 1/3 X^3 - 3/2X^2 +3

A:

Q: For the function f(x) = x3/3-x2- 24x + 19. what is the value over which the function is concave…

A: fx=x33-x2-24x+19    Now, first derivative is  dfdx=ddx(x33-x2-24x+19)  dfdx=x2-2x-24    And, second…

Q: f(x) = (4x2 – 5x)e"

A:

Q: (1) Find the domain of the function H(x) = x² – 4x

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the function f(x) = -4x^2 + 3x-1 1. F(-2)

A:

Q: Let f(x) = 2x - 5. g(x) = 4x - 1, h(x) = x2 + x + 2. Evaluate the function (g ∘ f)(0) without…

A: Consider the function: fx=2x-5,  gx=4x-1,  hx=x2+x+2

Q: 1. When the function f(x) is divided by x + 2, the quotient is x2 -x -8 and the remainder is -3.…

A:

Q: Determine the domain and range of the quadratic function. f (x) = –4(x + 1)² – 5 Enter your answer…

A: Givenf(x)=-4(x+1)2-5

Q: - 5x + 9 x 3 -

A:

Q: nd the y coordinate of the point of inflection of the function f(x)=x3-x2

A:

Q: f(x) = x²+6x+5 2-1

A: I am attaching image so that you understand each and every step.

Q: or what value of X does the function g(x) = 1/3 X3 - 2x2 attain the point of inflexion?

A:

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.