Application of Derivatives — Class 12 Mathematics PYQs

What is the maximum value of $a\cos x+b\sin x+c$?

The non-negative values of $b$ for which the function $\frac{16x^3}{3}-4b{x}^2+x$ has neither maximum nor minimum in the range $x>0$ is

Consider the following for the next two (02) items that follow:

Let $f(x)=\frac{x}{\ln x};(x>1)$

Consider the following statements:

1. $f(x)$ is increasing in the interval $(e,\infty )$
2. $f(x)$ is decreasing in the interval $(1,e)$
3. $9\ln 7>7\ln 9$

Which of the statements given above are correct?

Consider the following for the next two (02) items that follow:

A differentiable function $f(x)$ has a local maximum at $x=0$. Let $y=2f(x)+ax-b$.

The function $y$ has a relative maxima at $x=0$ for

Consider the following for the next two (02) items that follow :

Consider the function
$f(x)=|x-2|+|3-x|+|4-x|$, where $x\in \mathbb{R}$.

At what value of $x$ does the function attain minimum value?

Consider the following for the next two (02) items that follow :

Consider the function
$f(x)=|x-2|+|3-x|+|4-x|$, where $x\in \mathbb{R}$.

What is the minimum value of the function?

Consider the following for the next two (02) items that follow :

A function is defined by $f(x)=\left|\begin{array}{ccc}x+1& 2& 3\\ 2& x+4& 6\\ 3& 6& x+9\end{array}\right|$.

The function is decreasing on :

Consider the following for the next two (02) items that follow :

A function is defined by $f(x)=\left|\begin{array}{ccc}x+1& 2& 3\\ 2& x+4& 6\\ 3& 6& x+9\end{array}\right|$.

The function attains local minimum value at :

Consider the following for the next two (02) items that follow :

Given that $4x^2+y^2=9$.

What is the maximum value of $y$ ?

Consider the following for the next two (02) items that follow :

Given that $4x^2+y^2=9$.

What is the maximum value of $xy$ ?