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Understanding Arithmetic Progressions (AP) and Solving AP Problems
9:32 am | October 11, 2023
Definition of an Arithmetic Progression (AP) An arithmetic progression is a sequence of numbers (infinite or finite) where, starting from the second term, each term is the sum of the…

Finding the maximum and minimum values of functions
3:55 pm | October 1, 2023

Exploring Extremum Problems in Calculus: Finding Optima in Functions
8:37 am | September 18, 2023

Methods for finding extrema of functions
8:29 am | September 18, 2023

Application Exercises of Sum and Difference Formulas
8:22 am | September 18, 2023

EXERCISE

Find the set of all real values of the parameter \(m\) for which the function \(y = – {x^3} – 6{x^2} + \left( {4m – 9} \right)x + 4\) is strictly decreasing over the interval \(( – \infty, -1)\).

8:49 am | September 19, 2023

How many integer values of \(m\) make the function \(y = \left( {{m^2} – 1} \right){x^3} + \left( {m – 1} \right){x^2} – x + 4\) strictly increasing over \(\mathbb{R}\)?

8:35 am | September 19, 2023

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Understanding Arithmetic Progressions (AP) and Solving AP Problems
Finding the maximum and minimum values of functions
Find the set of all real values of the parameter \(m\) for which the function \(y = – {x^3} – 6{x^2} + \left( {4m – 9} \right)x + 4\) is strictly decreasing over the interval \(( – \infty, -1)\).
How many integer values of \(m\) make the function \(y = \left( {{m^2} – 1} \right){x^3} + \left( {m – 1} \right){x^2} – x + 4\) strictly increasing over \(\mathbb{R}\)?
Exploring Extremum Problems in Calculus: Finding Optima in Functions

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