A stationary point is a point on a curve where the derivative of a function is zero. It shows where the slope of the tangent becomes zero and the function is neither increasing nor decreasing. Stationary points can be local maxima or minima or points of inflection and are important for analyzing functions.
Class 12 Maths Chapter 6 focuses on Applications of Derivatives for CBSE Exam 2024-25. It includes rate of change of quantities increasing and decreasing functions tangents and normals maxima and minima. These concepts are applied to solve real-life problems in various fields like physics and economics while improving analytical skills and logical reasoning.
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To find the stationary points of the function f(x) = x³ – 3x² – 9x – 7, one would first have to compute the derivative of the function and set the function equal to zero. Stationary points occur at places where the derivative is equal to zero.
First, differentiate f(x):
f'(x) = d/dx(x³ – 3x² – 9x – 7) = 3x² – 6x – 9
Now, put f'(x) = 0 to get the stationary points:
3x² – 6x – 9 = 0
Divide the equation by 3:
x² – 2x – 3 = 0
Factor the quadratic equation:
(x – 3)(x + 1) = 0
Therefore, the solutions are x = 3 and x = -1.
Hence, the stationary points are at x = -1 and x = 3.
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