Question

Let f(x) = 8secx. Then f''(π/9) is:

A) 0
B) 8
C) 16
D) -8

Answer 1

The answer of the given equation that " f''(π/9) is" is C) 16

Step-by-step explanation:

To find the second derivative of
`\( f(x) = 8\sec(x) \),` we'll need to find the first derivative and then take the derivative again.

Given:

`\[ f(x) = 8\sec(x) \]`

First derivative
`\( f'(x) \):`

`\[ f'(x) = 8 \sec(x) \tan(x) \]`

Now, take the second derivative
`\( f''(x) \):`

`\[ f''(x) = 8 \sec(x) \tan(x) \tan(x) + 8 \sec(x) \sec(x) \]`

Now, evaluate
`\( f''(\pi/9) \):`

`\[ f''(\pi/9) = 8 \sec(\pi/9) \tan(\pi/9) \tan(\pi/9) + 8 \sec(\pi/9) \sec(\pi/9) \]`

The expression simplifies to
`\( 16 \),`so the correct answer is C) 16.