The height of a right triangle is 44 feet more than three times the length of its base. Express the area of the triangle as a function of the length of its base, x, in feet.   F(x)

Q: determine where the function is concave upward and where it is concave downward    g(x)= -X^2+7x+8

A:

Q: Differentiate the function. f(x)  = x5 + 5x

A: Given function:

Q: The total revenue for Fred's Estates LLC is given as the function R(x)=400x−0.2x2, where x is the…

A: Given  R(x)=400x-0.2x2

Q: Consider the function:  f(x)=5x+2   and   g(x)=3x-4  Solve for - (f°g) (x)

A: Given:

Q: The function f (x) = 1.8x +32 is used to convert temperature in Celsius temperature x to temperature…

A:

Q: Find the domain of the function f(x) = √(25 − x2).

A: The given function is fx=25-x2

Q: Determine where the function is concave upward and where it is concave downward. g(x) = -x² + 9x + 3

A: if second derivative is positive in any interval then f(x) has cancave upward  if second derivative…

Q: Find the the domain of the function f(x) x + 3 x2 + 10x 11 -

A: Given function is  f(x)=x+3x2+10x-11 Which is not defined if denominator part equals to zero.

Q: Find the domain and range of the function. f(x) = 1/x2

A:

Q: Find f'(x) when f(x) = (x+ + 3x)*. 43

A:

Q: Differentiate the function with respect to the independent variable. f(x) = (6 - 5x²) ³ f'(x) =O

A: Given, fx=46-5x23

Q: Find the points of inflection of the function f(x)=x2 / 1+x2.

A:

Q: Differentiate the function. f(x) (9x2 15x)e* = f'(x)

A: First simplify the given function as follows.

Q: The range of a function f(x) = 9x – 15 is {-42,39}. Wh %3D

A: Actually from my point of view you want to know the domain of f(x)  because in this question range…

Q: Find the value of the constant (a, b, or c) that makes the function continuous.

A: for the function f(x) to be continuous, the f(x) must be continuous at x=3Then,2x+9x-1 =-4x+c2x+9x…

Q: Determine where the function is concave upward and where it is concave downward. g(x) = 5x^3 = 6x

A: Find double derivative and put it equal to zero to find inflection point.  g'(x) = 15x^2 - 6 g''(x)…

Q: Find the domain of the function.

A: Given function, f(x)=x+2x-10

Q: Differentiate the function. y = (x+2)(x² + 2x +1)

A:

Q: Consider the function below. x2 – 2x + 1 f(x) 2x – 8

A:

Q: find the value of the constant (a, b, or c) that makes the function continuous. (x2 - c 4x + 2c for…

A: For limits to be continuous left hand limit must be equal to right hand limit and equal to limit at…

Q: Find the domain of the function f(x) = 3x+6.

A: Given function is fx=3x+6 We have to find domain of given function. Domain is the input value for…

Q: f(x) = 3 – 2x +x

A:

Q: For what value of x does the function g(x) = -x – 2x? attain the point of inflexion?

A: i have used the necessary and sufficient condition for point of inflection and obtained x=2 is…

Q: Consider the function f (x) = 3x – 6|. -

A: Given problem:- f(x) =|3x-6|  To find:- How is differentiability related to limits Rewrite f (x) as…

Q: Find the domain of the function. f(x) = 10(x + 6)

A:

Q: Determine where the function is convace upward   f(x)=-5x2-8x+5

A: A function is concave upward when it's second derivative is greater than zero. If the second…

Q: Find the inflection points for the function f(x) = 2x6 + 3x5 – 10x*. -

A: Note :- Inflexian points of a function can be calculate by putting f"(x) =0 and solve for x.  We get…

Q: How many points of inflection does the function f(x)=x7-x2 have?

A: We have to find number of inflection point for the function: fx=x7-x2 We know that inflection points…

Q: Find the domain and range of the function. f(x) = 3x

A: Given: f(x) = 3x To find: Domain and range of the given function.

Q: Find the slope of the graph of the function at the given value. f(x)= 2x² + 4 when x = 5

A: Slope of graph of function at given point is first derivative of function at that point.

Q: Find the domain of the function. f(x) = x / √(x + 8)

A:

Q: find inflection point for the function f(x)=x^3-6x^2+15

A: we have to find the point of infection for the given function

Q: Differentiate the function with respect to the independent variable. f(x) = (x° - 7x) 5 f'(x) = D

A: Given:

Q: Differentiate the function and simplify. f (x)= 42x-4x+1

A: We have to differentiate the function: fx=42x3-4x+1 In such cases we need to use logarithmic…

Q: Determine where the given function is concave up and where it is concave down  F(x)=10x3-3x5

A:

Q: Describe the concavity for the function f(x) = x³ – 3x.

A:

Q: Find the slope of the graph of the function at the given value. f(x) = 4x+ 8. when x = 5 %3D

A:

Q: Find the points of inflection of the function f(x)=x3−3x2−1.

A: Given

Q: Find the inflection points of the function f(x)=x+x5/3.

A: Inflection points are the points where the second derivative is zero. So differentiating with…

Q: How many points of inflection does the function f(x)=x8-x2 have?

A:

Q: Find the domain of the function: f(x) = 2(x + 5)

A: Given: fx=2x+5

Q: Differentiate the function: f(x) = √(1+3e4x)

A:

Q: Find the slope of the graph of the function f (x) 4(5x + 6)² at x = 3.

A:

Q: Where is the function concave upward and concave downward? f(x)=5x^7-28x^5

A: The given function is,

Q: Find the domain of the function.

A: Given, h(x)=4-x+x2-1

Q: Differentiate the function with respect to the independent variable. f(x) = - 3x° + 4x$ – 7

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.