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UPSC NDA I 2016 Mathematics Solved Paper

Question Numbers: 68-69

Direction: For the next two (2) items that follow:

Consider the function

f(x) = \left| x^{2} - 5x + 6 \right|

Question : 69 of 120

Marks: +1, -0

What is f’’(2.5) equal to?

Solution:

Concept:

The second derivative

f''(x)

is the derivative of the first derivative

f'(x)

Explanation:

For

x

between 2 and 3,

g(x)

is negative, so the function near

x = 2.5

f(x) = -x^2 + 5x - 6

First, differentiate

f(x)

f'(x) = \frac{d}{dx}(-x^2 + 5x - 6) = -2x + 5

Then differentiate

f'(x)

f''(x) = \frac{d}{dx}(-2x + 5) = -2

This second derivative is constant, so at

x = 2.5

f''(2.5) = -2

Answer:

-2

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