Find the tangent line

Question

Can someone help me understand tangent lines? Here is a question I'm struggling with. Thanks.

Derivative of the function g(x) 2x^3-4x is G(x)=6x^2-4

Find the equation of the tangent line to the fuction g(x) at x=1 Answer in Slope-intercept form.

Answer 1

y=2x^3-4x;                        x0=1

y'=6x^2-4

tangent lines

y=f '(x0)(x-x0)+y0

yo=2*1^3-4*1=-2

f '(x0)=6*1^2-4=2

then tangent lines

y=2*(x-1)-2

y=2x-4

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