What is the slope of the tangent at x=Pi/6 for f(x)=sin^2x-x=?

Question

What is the slope of the tangent at x=Pi/6

for f(x)=sin^2x-x=?

Answer 1

Answer 2

For equation of a line,you need:

1. a point
2. slope

point x = pi/6 ; f(pi/6) = sin( 2* pi/6) - pi/6 = (3)^(1/2)/2 - pi/6

slope = derivative at pi/6

fPrime(x) = 2cos(2x) -1

fPrime(pi/6) = 2 * cos(pi/3) - 1 = 0

Equation of the tangent:

y -y1 = m (x - x1)

y - [(3)^(1/2)/2 - pi/6] = 0 (x - pi/6)

y = (3)^(1/2)/2 - pi/6

it is a constaant line.

Ans:

y = (3)^(1/2)/2 - pi/6