Class 12th Mathematics, Tangent and Normals
Slopes of the Tangent and the Normal
1. Concept Overview At any point on a curve, the tangent is a line that just “touches” the curve locally…
Class 12th Mathematics, Tangent and Normals
Slope (Gradient) of a line
1. Definition Slope (or gradient) of a line refers to how steep the line is. It measures change in y
Class 12th Mathematics, Rolles and Lagranges Theorem
How to Verify Lagrange`s Mean Value Theorem
Practice Questions With Step-by-Step Solutions Question 1 Verify LMVT for [f(x)=x^{2}-2x] on [[0,3]]. Step-by-Step Solution: Polynomial → continuous & differentiable
Class 12th Mathematics, Rolles and Lagranges Theorem
Lagrange`s Mean Value Theorem
1. Statement of the Theorem If a function [f(x)] satisfies: It is continuous on the closed interval [[a,b]], and It
Class 12th Mathematics, Rolles and Lagranges Theorem
How to Verify Rolle`s Theorem
Practice Questions With Step-By-Step Solutions Question 1 Let [f(x)=x^{3}-3x^{2}-x+3] on [0,3]. Show Rolle’s Theorem applies and find [c]. Step-by-step Solution
Class 12th Mathematics, Rolles and Lagranges Theorem
Rolle`s Theorem
1. Statement of the Theorem If a function [f(x)] satisfies all the following three conditions on the closed interval [a,b]:
Class 12th Mathematics, Derivative as Rate Measure
Example 1 – Derivative as a Rate Measure
Practice Questions with Step by Step Solutions Question 1 A particle moves so that its position is [s(t)=3t^{3}-9t^{2}+6t] (metres). Find
Class 12th Mathematics, Derivative as Rate Measure
Derivative as a Rate Measure
1. Concept Overview A derivative represents how fast one quantity changes with respect to another. If we have a function:
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