NDA Mathematics 21 April 2024 | Application of Derivatives Question 4 | Mathematics

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

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

Which of the following is/are correct?

1. $f'(0) = 0$

2. $f''(0) < 0$

Select the correct answer using the code given below:

1 only

2 only

Both 1 and 2

Neither 1 nor 2

NDA Mathematics 21 April 2024

MCQ (Single Correct Answer)

+2.5

-0.83

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

$a > 0, \ b = 0$

for all $b$ and $a = 0$

for all $b > 0$ only

for all $a$ and $b = 0$

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next items that follow:

Given that 4x2 + y2 = 9.

What is the maximum value of y?

$\frac{3}{2}$

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following for the next items that follow:

Given that 4x2 + y2 = 9.

What is the maximum value of xy ?

$\frac{9}{4}$

$\frac{3}{2}$

$\frac{4}{9}$

$\frac{2}{3}$

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