Find equation of tangent line...?

Question

How do I find an equation of a tangent line to the curve at the given point:

y = sec(x) (Pi/3,2)

what are the steps?

Answer 1

y=sec x

dy/dx= sec x * tan x

Plug in pi/3 into the dy/dx and you will get a slope m= 2*3^(1/2)

Use the point slope form: Y-Y0= m(x-x0)

y-2= 2*3^(1/2) (x - pi/3). You can also put this into slope intercept form. These sites will help you.

Answer 2

y= sec x
where x= pi/3 and y= 2

1st, we need to get the slope
slope can be the differential of the equation
y= secx
y'= sec x tan x dx
the differential of secx is secxtanx

we substitute pi/3 top the equation y'= secxtanx dx
x=pi/3
dx=0, because the differential of a constant is always zero, or 1
y'= 2 square root of 3

so
equation of tangent
y=m(x-pi/3) +2

Answer 3

slope =m=dy/dx=secx*tanx=2 * 3^1/2

equation of tangent
y-2=m(x-pi/3)

Answer 4

I take it you comprehend derivatives. f(x)= (x^3 - x^2 + x)^8so discover f '(x) f '(x)=8(x^3 - x^2 + x)^7*(3x^2-2x+a million) it extremely is through the chain rule g(x)^8=8*g(x)^7*g '(x) now you want the slope while x=a million so f '(a million)=sixteen now you want a line by (a million,a million) and slope sixteen so we use our factor slope type with m=sixteen and factor (a million,a million) y – y1 = m(x – x1) and x1=y1=a million so y-a million=sixteen(x-a million) or y-a million=16x-sixteen or y=16x-15 is the line by a million,a million and tangent to the given f(x).

Answer 5

dy / dx = tan x.sec x
At x = π/3:-
dy/dx = (√3/2) x 2 = √3 = m,say
Tangent passes thro` (π/3 , 2)
Equation of tangent line is:-
y - 2 = √3.(x - π/3)
y = √3.x + (2 - π/√3 )