I need help to find the tangent line of this equation?

The equation is f(x) = 3x+(4/x) at x =-3

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A few days ago

Anonymous

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You just need to calculate the derivative at x=-3. You then have the slope and a point, which is enough to determine the formula for a line.

f(x) = 3x + 4/x = 3x + 4x^-1

df(x)/dx = 3 – 4x^-2

df(-3)/dx = 3 – 4/9 = 23/9

Equation of a line is y=mx + b

f(-3) = 3(-3) + 4/(-3) = -9 – 4/3 = -31/3

The point that the tangent line must pass through is (-3,-31/3)

Subsituting: -31/3 = 23/9 * (-3) + b

b = -8/3

Therefore the equation of the tangent line is:

y = 23x/9 – 8/3

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