Real values refer to all numbers on the number line, including rational and irrational numbers. They represent quantities that can exist in the real world, such as measurements, distances, and physical properties. Real values are used to solve equations, model phenomena and analyze functions, forming the foundation of calculus, algebra and applied mathematics.
Class 12 Maths Chapter 6 deals with Applications of Derivatives for CBSE Exam 2024-25. It covers rate of change of quantities increasing and decreasing functions tangents and normals maxima and minima. These topics are essential to solve problems in physics economics and engineering while enhancing analytical skills and practical understanding of mathematical concepts.
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The function f(x) = |x| is neither increasing nor decreasing throughout its domain since:
– For x ≥ 0, the function is increasing (since f(x) = x for nonnegative x).
– For x < 0, the function is decreasing (since f(x) = -x for negative x).
The function is neither strictly increasing nor strictly decreasing at x = 0 because of a sharp "corner."
Hence f(x) = |x| is neither increasing nor decreasing on its entire domain.
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