Question

Find the equation of the line tangent to the function: f(x)=2cos(3x) at the point x0=pi/2.

Answer 1

equation of tangent is y = 6x - 3π

we have to find the equation of line of tangent to the function, f(x) = 2cos(3x) at the point x = π/2.

differentiating f(x) with respect to x,

df(x)/dx = -6sin(3x)

slope of tangent at that point, m = -6sin(3π/2)

= -6sin(π + π/2) = -6(-1) = 6

y = f(π/2) = 2cos(3π/2) = 0

x = π/2

so, equation of tangent to the function at point x = π/2,

(y - 0) = 6(x - π/2)

y = 6x - 3π

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