What is the equation of the line tangent to # f(x)=-3x^4 -x^2 − 2x# at # x=1#?

1 Answer
Jim G.
Feb 16, 2017

#y=-16x+10#

Explanation:

The equation of the tangent in #color(blue)"point-slope form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where m represents the slope and # (x_1,y_1)" a point on the line"#

#color(orange)"Reminder " m_("tangent")=f'(x)" at x=a"#

#rArrf'(x)=-12x^3-2x-2#

#f'(1)=-12-2-2=-16=m_("tangent")#

#"and "f(1)=-3-1-2=-6#

#"Using "m=-16" and " (x_1,y_1)=(1,-6)#

#rArry+6=-16(x-1)#

#rArry=-16x+16-6#

#rArry=-16x+10" is the equation of tangent"#

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