Use the equation given below to find f''(π/4) . f(x) = sec(x)

Solution:

A derivative is the rate of change of a function with respect to another quantity.

Differentiation means the rate of change of one quantity with respect to another. 

Given, f(x) = sec(x)

f’(x) = sec(x) tan(x)

d/dx (sec(x)tan(x)) = sec(x) d/dx(tan(x)) + tan(x) d/dx(sec(x))

= sec(x) sec²(x) + tan(x) sec(x) tan(x)

f’’(x) = sec³(x) + tan²(x) sec(x)

Put x = π/4

f’’(π/4) = sec³(π/4) + tan²(π/4) sec(π/4)

= (√2)³ + (1)²(√2)

= 2√2 + √2

= 3√2

Therefore, f’’(π/4) = 3√2.

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Use the equation given below to find f''(π/4) . f(x) = sec(x)

Summary:

Given, f(x) = sec(x), then f’’(π/4) is 3√2.