What is the equation of the line tangent to #f(x)=2x^3 - 5/x # at #x=-1#?

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Answer 1 · 2016-01-10T12:35:54

Tangent Line

#y=11x+14#

#f(x)=2x^3-5/x# at #x=-1#

find #f(-1)#

#f(-1)=2*(-1)^3-5/-1#

#f(-1)=3#

first derivative

#"f' (x)= 6x^2+5/x^2#

#f'(-1)=6(-1)^2+5/(-1)^2#

#f' (-1) = 11# slope

The tangent line

#y-y_1=m(x-x_1#

#y-3=11(x-(-1))#

#y=11x+14#