What is the tangent of f(x)=5tan(x),\at x= pi/4 ?

The tangent of f(x)=5tan(x),\at x= pi/4 is y=10x+5-(5pi)/2

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tangent of f(x)=5tan(x),\at x= pi/4

tangent of

f (x) = 5 tan (x), at x = \frac{π}{4}

y = 10 x + 5 - \frac{5 π}{2}

Solution steps

Find the tangent point:

(\frac{π}{4}, 5)

Find the slope of

f (x) = 5 tan (x) : \frac{df ( x )}{d x} = 5 sec^{2} (x)

Compute the slope of

f (x) = 5 tan (x)

x = \frac{π}{4} : m = 10

Find the line with slope m=

10

and passing through

(\frac{π}{4}, 5) : y = 10 x + 5 - \frac{5 π}{2}

y = 10 x + 5 - \frac{5 π}{2}

5

\frac{d}{d x} (9 x - 45)

f (x) = 4 x^{- 3} + x^{2} + 14

\frac{d}{d x} (e^{- \frac{2}{3} x})

\frac{d}{d x} (\frac{x ^{2} - 2 x}{x})

What is the tangent of f(x)=5tan(x),\at x= pi/4 ?
The tangent of f(x)=5tan(x),\at x= pi/4 is y=10x+5-(5pi)/2