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Increasing and Decreasing Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIncreasing and Decreasing Functions3 Marks
Question
State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 - 6x + 3 is increasing on the interval [4, 6].
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Answer

A function f(x) is said to be increasing on an interval [a, b] if it is increasing at x = a and x = b.
Here,
f(x) = x2 - 6x + 3
f'(x) = 2x - 6
f'(x) = 2(x - 3)
Now, f'(4) = 2(4 - 3)
= 2
$\therefore$ f'(4) > 0
So, f(x) is increasing on x = 4
f'(6) = 2(6 - 3)
= 6
$\therefore$ f'(6) > 0
So, f(x) is increasing on x = 6
Hence, f(x) is increasing on [4, 6].

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