# If #f(x)=sec(x)#, how do I find #f''(π/4)#?

Evaluate:

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To find ( f''(\frac{\pi}{4}) ) for ( f(x) = \sec(x) ), you first need to find the first and second derivatives of ( \sec(x) ) with respect to ( x ).

The first derivative of ( \sec(x) ) is ( \sec(x) \tan(x) ).

The second derivative of ( \sec(x) ) is ( \sec(x) \tan(x) \tan(x) + \sec(x) \sec^2(x) = \sec(x)(\tan^2(x) + \sec^2(x)) ).

Now, evaluate ( f''(\frac{\pi}{4}) ) by substituting ( \frac{\pi}{4} ) into the second derivative expression.

( \sec(\frac{\pi}{4}) = \sqrt{2} ) and ( \tan(\frac{\pi}{4}) = 1 ).

So, ( f''(\frac{\pi}{4}) = \sqrt{2}(\tan^2(\frac{\pi}{4}) + \sec^2(\frac{\pi}{4})) = \sqrt{2}(1 + 2) = \sqrt{2}(3) = 3\sqrt{2} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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