Question

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

Answer 1

Answer:

The value of b is -12

Step-by-step explanation:

Differentiate the given function with respect to $x$.

$f'(x)=4x-4$

Subsitute $3$ for $x$ in $f'(x)$.

$f'(3)=4\cdot3-4\\=12-4\\=8$

The slope of a tangent line is $f'(3)=m=8$.

Subsitute $8$ for $m,$ $12$ for $y_1$ and $3$ for $x_1$ in $y-y_1=m(x-x_1)$.

$y-12=8(x-3)\\y-12=8x-24\\y=8x-24+12\\y=8x-12$

So, the value of $b$ is $-12$