# >Question 2 of 165лFind an equation of the tangent line to f(x) = 4 sec (x) at x =6(Express numbers in exact form. Use symbolic notation and fractions where needed. Express equation in terms of y and x,where y is the dependent variable and x is the independent variable.)equation:

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18 views help_outlineImage Transcriptionclose> Question 2 of 16 5л Find an equation of the tangent line to f(x) = 4 sec (x) at x = 6 (Express numbers in exact form. Use symbolic notation and fractions where needed. Express equation in terms of y and x, where y is the dependent variable and x is the independent variable.) equation: fullscreen
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Step 1

Given equation of curve is f(x)=4secx

We know that slope of tangent to curve y=f(x) at x=a is f'(a).Therefore , slope of tangent to given curve at x=5pi/6 can be caculated as help_outlineImage Transcriptionclosef(x)4 f'(x) =4secx = 4secx tan x 5л tan 6 2 1 m f = 4sec 4 fullscreen
Step 2

The y -coordinate of the point ,whose x-coordinate is 5pi/6 ,is f(5pi/6) help_outlineImage Transcriptionclose8/3 5л 5л 2 y = f 6 = 4sec 4 V3 6 3 3 fullscreen
Step 3

Now, we use slope-point form of equation of line to find ... help_outlineImage Transcriptionclosey (x-x 8/3 8 y + 57T x 3 &/3 8 y + 3 207 -x 9 207 83 y =x- 3 3 fullscreen

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