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Increasing and Decreasing Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIncreasing and Decreasing Functions3 Marks
Question
Show that f(x) = x9 + 4x7 + 11 is an increasing function for all $\text{x}\in\text{R}.$.
✓

Answer

f(x) = x9 + 4x7 + 11
f'(x) = 9x8 + 28x6
= x6(9x2 + 28)
Now,
$\text{x}\in\text{R}$
⇒ x6 > 0 and 9x2 + 28 > 0
⇒ x6(9x2 + 28) > 0
⇒ f'(x) > 0
So, f(x) is increasing on function for $\text{x}\in\text{R}.$

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