Find the intervals in which the function f given by f(x) = x² – 4x + 6 is strictly increasing:
An interval represents a set of numbers between two given values on a number line. It can be open closed or semi-open depending on whether the endpoints are included or not. For example the interval (2 5] includes all numbers between 2 and 5 except 2 but including 5.
Class 12 Maths Chapter 6 Applications of Derivatives is an important topic for the CBSE Exam 2024-25. It includes the rate of change of functions increasing and decreasing functions maxima and minima tangents and normals and approximations. These concepts are widely used in physics economics and engineering to solve real-world problems efficiently.
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To find the intervals where the function f(x) = x² – 4x + 6 is strictly increasing, we have to look at its derivative.
Find the derivative of the function:
f'(x) = d/dx(x² – 4x + 6) = 2x – 4
Determine where the derivative is positive (for strictly increasing behavior):
f'(x) > 0
2x – 4 > 0
x > 2
So, the function is strictly increasing when x > 2.
Conclusion:
The function is strictly increasing on the interval (2, ∞).
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