Trying to determine or know which is the graph of the equation:

from this group of graphs in the picture, we have to do some arithmetic work.

We shall begin by finding the y-intercept. The y-intercept is the value of f(x) when the value of x is equal to zero

The y-intercept is the value of f(x) when the value of x is equal to zero

For

Point

Then we have to find the value of f(x) for

Point

At this point, you have to plot a graph of points A and B to find the solution. Therefore we have the graph for the equation below.

Table of Contents

## What is calculus?

Calculus is a branch of mathematics that deals with the calculation of instantaneous rates of change (differential calculus), as well as the summation of an infinite number of small factors in order to determine some whole. In other words, calculus is a branch of mathematics that determines something by adding up a bunch of little things. Calculus, to put it another way, is a branch of mathematics that determines some whole by adding up an infinite number of factors that are relatively small (integral calculus).

Calculus was independently developed in the 17th century by two different mathematicians from different countries: Gottfried Wilhelm Leibniz of Germany and Isaac Newton of England. These two mathematicians were both based in Germany at one point or another. The development of calculus is typically attributed to both of these mathematicians, even though they did not collaborate with one another. Students who intend to major in physics, chemistry, biology, economics, finance, or actuarial science are now required to take calculus as part of their academic curriculum.

Calculus is a subject that must be covered for students who wish to pursue a minor in actuarial science. As a direct consequence of this, students who wish to enter these fields at the foundational level are required to have completed calculus. Calculus enables the solution of a wide variety of problems, such as the monitoring of the location of a space shuttle and the forecasting of the pressure that will build up behind a dam as the water level rises. In other words, calculus makes it possible to solve a lot of problems.

Without the use of calculus, neither of these problems could possibly be resolved. Calculus problems, which were once thought to be incapable of being solved, can now be solved with the assistance of computers, which are an extremely helpful tool. In the past, it was believed that calculus problems could not be solved.

## Differentiation and Integration

Both Newton and Leibniz independently developed simple rules for determining the formula for the slope of the tangent to a curve at any point along with it, given only the formula for the curve itself. These rules can be applied to determine the formula for the slope of the tangent at any point along the curve. These guidelines can be used to determine the behavior of the curve at any point along its path. The rate of change of a function, which is represented by the symbol f, is referred to as the derivative of the function, which is represented by the symbol f′.

Differentiation is the process of determining the formula of a function’s derivative, and the rules that govern differentiation are the basis of differential calculus. Differentiation is referred to as the process of differentiation. The fact that the results of differential calculus can be interpreted in a number of different ways, depending on the conditions of the problem, is the source of the subject’s power. The slopes of tangent lines, the velocities of moving particles, and other quantities can all be interpreted as derivatives, for example.

One of the most important applications of differential calculus is graphing a curve given its equation, which in this case is y = f. This is one of the most important parts of the subject (x). Two of the tasks involved in completing this process are locating the local points of maximum and minimum on the graph, as well as identifying changes in inflection (convex to concave, or vice versa). These geometric concepts all have physical interpretations, which allow a scientist or an engineer to quickly get a feel for the way a physical system behaves. Examining a function that is implemented in a mathematical model will result in the disclosure of these interpretations.

A principle that is now known as the fundamental theorem of calculus is the idea that the problem of determining the derivatives of functions is, in a very specific sense, the inverse of the problem of determining the areas under curves. This is now considered to be a well-established fact in the field of calculus. This was the other major finding that Newton and Leibniz made during their time together. Newton made the specific discovery that if there is a function F(t) that denotes the area under the curve y = f(x) from, say, 0 to t, then the derivative of this function will equal the original curve over that interval, and the equation for this derivative is F′(t) = f.

See also: **What is the value of a Constant term or Variable**

Newton also discovered that if there is a function that denotes the area under the curve y = f(x) from, say, 0 to t, Newton is widely regarded as the person responsible for this particular discovery (t). Therefore, in order to calculate the area that lies below the curve y = x2 from 0 to t, all that is required is to locate a function F such that F′(t) = t2, and that is all that is required for the calculation. The differential calculus demonstrates that the function x3/3 + C, where C can be any arbitrary constant, is the most general of these kinds of functions. This idea is referred to as the (indefinite) integral of the function y = x2, and its representation in mathematics is represented by the symbol x2dx.

The first symbol is an extended S, which stands for sum, and the dx symbol indicates an infinitely small increment of the variable, or axis, over which the function is being summed. The extended S represents the sum. These two symbols, when put together, form what is known as the sum symbol. Because Leibniz conceived of integration as the process of determining the area under a curve by adding the areas of an infinite number of infinitesimally thin rectangles that lie between the x-axis and the curve, he was the one who first proposed this concept.

This is because Leibniz conceived integration as the process of determining the area under a curve. Newton and Leibniz made the discovery that integrating f(x) is the same as solving a differential equation, which means finding a function F(t) such that F′(t) = f. This was an important step in the development of differential equations. This was a significant advance that was made toward the development of calculus (t).

Finding the distance traveled by an object whose velocity has a given expression can be interpreted in physical terms as finding the distance F(t) traveled by an object whose velocity has a given expression f when this equation is solved. In other words, finding the distance traveled by an object whose velocity has a given expression is the same as finding the distance traveled by an object whose velocity has a given (t).

Calculating integrals is the focus of the subfield of calculus known as integral calculus. Some of the many applications of integral calculus include determining the amount of work that is done by physical systems and the pressure that exists behind a dam at a specific depth.