matthewmcmahan693
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I really need help with figuring out how to calculate b, I've been really confused.

If f(x)=2x2−4x+6 , find f'(3) =8

Use this to find the equation of the tangent line to the parabola y=2x2−4x+6 at the point (3,12) . The equation of this tangent line can be written in the form y=mx+b where m is: 8

and where b is:

I really need help with figuring out how to calculate b Ive been really confused If fx2x24x6 find f3 8 Use this to find the equation of the tangent line to the class=

Respuesta :

Answer:

The value of b is -12

Step-by-step explanation:

Differentiate the given function with respect to [tex]x[/tex].

[tex]f'(x)=4x-4[/tex]

Subsitute [tex]3[/tex] for [tex]x[/tex] in [tex]f'(x)[/tex].

[tex]f'(3)=4\cdot3-4\\=12-4\\=8[/tex]

The slope of a tangent line is [tex]f'(3)=m=8[/tex].

Subsitute [tex]8[/tex] for [tex]m,[/tex] [tex]12[/tex] for [tex]y_1[/tex] and [tex]3[/tex] for [tex]x_1[/tex] in [tex]y-y_1=m(x-x_1)[/tex].

[tex]y-12=8(x-3)\\y-12=8x-24\\y=8x-24+12\\y=8x-12[/tex]

So, the value of [tex]b[/tex] is [tex]-12[/tex]

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