Write an equation for the line tanget to the curve y=2tan(pix/4) at x=1

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The slope of a tangent drawn to y = f(x) at x = c is given by f'(c).

Here `y = 2*tan(pi*x/4)` and the equation of the slope has to be determined at x=1

y' = `2*(pi/4)*sec^2(pi*x/4)`

At x = 1 this is equal to `2*(pi/4)*(1/2) = pi/4`

At x = 1, `y = 2*tan (pi/4)` = 2

The equation of the tangent is `(y - 2)/(x - 1) = pi/4`

=> `y - 2 = (pi/4)*x - pi/4`

The required tangent is `y - 2 = (pi/4)*x - pi/4`

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