Class 12th Mathematics, Increasing and Decreasing Function
Decreasing Function
1. Concept Overview A function describes how one quantity changes with respect to another. A function can decrease, meaning its…
Class 12th Mathematics, Increasing and Decreasing Function
Increasing Function Example
Question 1. Determine where [f(x)=x^{3}-3x] is increasing. Step-by-step Solution: [\dfrac{d}{dx}f(x)=3x^{2}-3]. Solve [3x^{2}-3=0] ⇒ [x^{2}=1] ⇒ [x=\pm 1]. Sign chart for
Class 12th Mathematics, Increasing and Decreasing Function
Increasing Functions
1. Concept Overview A function is said to be increasing when its output rises as the input increases. Formally: A
Class 12th Mathematics, Tangent and Normals
Example Set 1 – Equation of the Tangent and the Normals
Practice Questions with Step-by-Step Solutions Question 1 Find the equation of the tangent and the normal to [y = x^{2}
Class 12th Mathematics, Tangent and Normals
Equations of the Tangents and the Normals
1. Concept Overview For a curve represented by [y=f(x)], the tangent at a point is a straight line that just
Class 12th Mathematics, Tangent and Normals
Example Set 1 – Tangents and Normals
Practice Questions with Step-by-Step Solution Question 1 Curve: [y = x^{2}] at [x = -2]. Find tangent slope, normal slope,
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
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