Tangent Line Calc

Question

let f(x) = (2sinx)/(4sinx+6cosx)

the f'(x)= 12/(4sin(x)+6cos(x))^2

the equation of the tangent line y=f(x) at a pi/2 can be writen in y=mx+b form

m=

b=

Answer 1

The derivative is correct, so to find slope of the tangent line:

m = 12/[4sin(pi/2)+6cos(pi/2)]²=12/[4]²=12/16=3/4.

Find f(pi/2) to determine y-coordinate of point of tangency:

f(pi/2) = 2sin(pi/2) / [4sin(pi/2) +6cos(pi/2)] = 2/[4+0] = 1/2

Using point slope:

y - 1/2 = (3/4) (x - pi/2)

y = (3/4)(x - pi/2) + 1/2

Now distribute the 3/4 and write the constant as a single fraction.

Check your work here:

desmos.com/calculator/1yzhsgwbwy