What is the tangent of f(x)=6sec(x),\at x= pi/3 ?

The tangent of f(x)=6sec(x),\at x= pi/3 is y=12sqrt(3)x+12-4sqrt(3)pi

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tangent of f(x)=6sec(x),\at x= pi/3

tangent of

f (x) = 6 sec (x), at x = \frac{π}{3}

y = 123 x + 12 - 43 π

Solution steps

Find the tangent point:

(\frac{π}{3}, 12)

Find the slope of

f (x) = 6 sec (x) : \frac{df ( x )}{d x} = 6 sec (x) tan (x)

Compute the slope of

f (x) = 6 sec (x)

x = \frac{π}{3} : m = 123

Find the line with slope m=

123

and passing through

(\frac{π}{3}, 12) : y = 123 x + 12 - 43 π

y = 123 x + 12 - 43 π

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What is the tangent of f(x)=6sec(x),\at x= pi/3 ?
The tangent of f(x)=6sec(x),\at x= pi/3 is y=12sqrt(3)x+12-4sqrt(3)pi