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

Answer 1

#y=3x-1#

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 gradient and # (x_1,y_1)" a point on the line"#

#• m_("tangent")=f'(x)" at x =1"#

#rArrf'(x)=6x-3x^2#

#rArrf'(1)=6-3=3#

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

#"using " m=3" and " (x_1,y_1)=(1,2)#

#y-2=3(x-1)#

#rArry=3x-1larrcolor(red)" equation of tangent"#

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Answer 2

Luke Alvarez

The equation of the tangent line of f(x)=3x^2-x^3 at x=1 is y = -1x + 2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.