Mathematics
Calculus and Rates of Change
Calculus here is the math of change, in two topics. Introduction to Derivatives, for grade 12, builds the derivative from the average rate of change, then the rules, the tangent line and a first study of a function. Single-Variable Calculus, a first-year university course, makes the limit precise and defines the integral before computing it. Lessi, an AI teacher, teaches both live.
- Topics
- 15
- Ages
- Grade 12
Areas of Mathematics
Topics in Calculus and Rates of Change1–15 of 15
- What is an average rate of change?The average rate of change measures how much a function changes per unit of input over a given interval. Mathematically, it is the difference in function values divided…Read the topic
- What is the derivative of a function at a point?The derivative of a function at a point is the instantaneous rate of change of the function at that exact input. Geometrically, it is the slope of the tangent line to the…Read the topic
- How do you differentiate a polynomial?Differentiating a polynomial involves applying the power rule to each term individually. Multiply each coefficient by its variable's current exponent, reduce that…Read the topic
- When do you use the product, quotient and chain rules?You use the product rule when two variable expressions are multiplied together, the quotient rule when one variable expression is divided by another, and the chain rule…Read the topic
- How do you find the equation of a tangent to a graph?To find the equation of a tangent to a graph, find the y-coordinate by plugging the x-value into the original function, find the slope by plugging the x-value into the…Read the topic
- How do you find intervals of increase and decrease and points of extremum?To find intervals of increase and decrease and points of extremum, calculate the first derivative f'(x), set it equal to zero, and solve for candidate values. Test the…Read the topic
- How to find inflection points?You can find an inflection point on a function by calculating the second derivative, setting it equal to zero, and solving for x. Next, check whether the second…Read the topic
- How do you find velocity and acceleration from position?To find velocity from a position function s(t), take its first derivative with respect to time: v(t) = s'(t). To find acceleration, take the derivative of velocity, which…Read the topic
- How do you find an antiderivative?Finding an antiderivative of a function means reversing the process of differentiation. For any polynomial term ax^n, add 1 to the exponent and divide the coefficient by…Read the topic
- How to find the area under a curve?You find the area under a curve y = f(x) above the x-axis between two vertical lines x = a and x = b by evaluating the definite integral of f(x) from a to b. First find…Read the topic
- How do you find the area below the x axis?To find the geometric area when a curve lies below the x-axis, calculate the definite integral over the interval and take its absolute value. Because the definite…Read the topic
- How to find the area between two curves?You calculate the area bounded by two curves by integrating the difference between the upper and lower functions. First, identify their intersection points to set your…Read the topic
- How to find a function from its derivative and a point?To recover the original function, integrate its derivative to get an equation with an unknown constant C. Then, substitute the coordinates of the given point into this…Read the topic
- How do you integrate roots and powers?Integrating expressions with roots and powers begins by converting roots into fractional exponents and reciprocals into negative exponents. Next, apply the power rule:…Read the topic
- How do you find the volume of a solid of revolution?To find the volume of a solid of revolution rotated around the x-axis, slice the shape into infinitely thin circular discs of radius r = f(x) and thickness dx. The volume…Read the topic
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יוחאי אCalculus teacherרמת גןסטטיסטיקאי ומוסמך MBA מסייע בעיבודים סטטיסטיים ומעביר שיעורים פרטיים (ליחיד או לקבוצות קטנות).Full profile
אבירם יעקביאןCalculus teacher₪230 / hourראשון לציוןבוגר מתמטיקה בהצטיינות מהטכניון, מרצה ומתרגל מצטיין. בעל ניסיון עשיר ורב שנים. מלמד מתמטיקה בגובה העיניים, סבלני ואיכפתי:)Full profile
יונתן סברדלובCalculus teacher₪200 / hourראשון לציוןמסיים דוקטורט במתמטיקה ומדעי המחשב, עם ניסיון רב בהוראה לסטודנטים. רגוע, סבלני ואוהב ללמד, עם דגש על הסברים ברורים, השלמת פערים והכנה ממוקדת למבחנים.Full profile
תמיר גבעוןCalculus teacher₪150 / hourבאר שבעמהנדס תוכנה, נותן שיעורים פרטיים בפיסיקה, מתמטיקה ושפות תכנות.Full profile
גד צומאיCalculus teacher₪200 / hourתל אביב -יפואני גד, בוגר הנדסת תוכנה בטכניון. בעל נסיון עשיר בהכנה לבגרויות, פסיכומטרי, ולקורסי המתמטיקה והפיסיקה בהנדסה.Full profile
יאיר לביאCalculus teacher₪150 / hourכפר סבאשעורים פרטיים במתמטיקה, סטטיסטיקה ופיסיקה לסטודנטים בכל החוגים + הכנה לבגרות לתלמידי תיכון. המורה בעל תואר שני ונסיון רב.Full profile
אליהו רושהCalculus teacher₪160 / hourירושליםבס"ד בוגר תואר ראשון במתמטיקה מהטכניון, מעל 16 שנים ניסיון בשיעורים פרטיים. שיעורים בכל הרמות- בגרויות עד סטודנטים בתואר ראשון.Full profile
עמרי שפרCalculus teacher₪170 / hourירושליםסטודנט תואר שני להנדסת גרעין כימית בחו"ל, עם נסיון של שנים בהוראת מתמטיקה ומדעים באופן פרטי וכמורה בבתי ספר. כרגע בשל התואר מלמד רק בזום.Full profile
About Calculus and Rates of Change
The grade 12 course starts with the slope of a chord, moves it until it becomes a tangent, and calls the result a derivative. From there come the differentiation rules and the first steps in studying a function. The university course goes back to the foundations: the epsilon-delta limit, continuity and the intermediate value theorem, the derivative as a limit, and the Riemann integral defined before it is computed.
Calculus also runs through the four- and five-unit math bagrut courses, which are listed under algebra. Lessi teaches each topic live: on a board, out loud, with short quizzes, at the student's pace, and the first 60 minutes with Lessi are free with an account.