Let f(x)= | cc x^2 & x p & -1 |, where p is a constant. The value… - Vidyadip

MCQ

Let $f(x)=\left|\begin{array}{cc}x^2 & \sin x \\ p & -1\end{array}\right|$, where $p$ is a constant. The value of $p$ for which $f^{\prime}(0)=1$ is

A
$R$
B
$1$
C
$0$
✓
$-1$

✓

Answer

Correct option: D.

$-1$

Given, $f(x)=\left|\begin{array}{cc}x^2 & \sin x \\ p & -1\end{array}\right|=-x^2-p \sin x$
$\Rightarrow f^{\prime}(x)=-2 x-p \cos x$
We have $ f^{\prime}(0)=1$
$ \Rightarrow-2(0)-p \cos (0)=1 $
$\Rightarrow-p=1 $
$\Rightarrow p=-1$

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