A few days ago
I need help to find the tangent line of this equation?
The equation is f(x) = 3x+(4/x) at x =-3
Top 1 Answers
A few days ago
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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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