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Differentiation — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDifferentiation1 Mark
MCQ
If $f(x) = |x^2 - 9x + 20|,$ then $f(x)$ is equal to:
  • A
    $-2x + 9$ for all $\text{x}\in\text{R}$
  • B
    $2x - 9$ if $4 < x < 5$
  • ✓
    $-2x + 9,$ if $4 < x < 5$
  • D
    None of these.
✓

Answer

Correct option: C.
$-2x + 9,$ if $4 < x < 5$
We have, $f(x) = |x^2 - 9x + 20|$
$\text{f}(\text{x})=\begin{Bmatrix} \text{x}^2-9\text{x}+20, & -\infty<\text{x}\leq4 \\ -\big(\text{x}^2-9\text{x}+20\big), & 4<\text{x}<5 \\ \text{x}^2-9\text{x}+20, & 5\leq\text{x}<\infty \end{Bmatrix}$
$\Rightarrow\text{f}'(\text{x})=\begin{Bmatrix} 2\text{x}-9\text{x}, & -\infty<\text{x}\leq4 \\ 2\text{x}-9, & 4<\text{x}<5 \\ 2\text{x}-9, & 5\leq\text{x}<\infty \end{Bmatrix}$
$\therefore f'(x) = -2x + 9$ for $4 < x < 5$

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