Answer :
The required slope of the tangent line to f(x) = 6 sin(x) at x = π/6 is 3 √3.
What is slope?
The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.
The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,
m = (y₂ - y₁)/(x₂ - x₁)
The slope is also denoted by tan θ.
The given equation of line,
f(x) = 6 sin(x)
To find the slope of the given line, differentiate with respect to x,
f'(x) = tan θ = d/dx(6 sin(x))
= 6 d/dx(sin(x))
= 6 cos x
At x = π/6, the slope of line,
f'(π/6) = 6 cos(π/6)
= 6 (√3 / 2)
= 3 √3
The slope of the tangent line to f(x) = 6 sin(x) is 3 √3.
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