Question

f(x)=(3x^2-2x-1) find equation of the line that is tangent and parallel to this line 8x-2y+12=0

Answer 1

wait to which line?
f(x)=(3x^2-2x-1)
or
8x-2y+12=0?

Answer 2

8x-2y+12=0 cant figure it out because i need the two points (x and Y) my book is not clear

Answer 3

howdy. First we can find the slope of the line. I'll rewrite it in y=mx+b form to make it apparent: y = 4x+6 -> slope is 4

Answer 4

Then we need to find where the derivative (slope of the tangent) is equal to 4

Answer 5

The derivative is: f'(x)=6x-2
4=6x-2 -> x = 1

Answer 6

This means that the tangent line to f(x) at x = 1 has a slope of 4 and is thus parallel to the given line. Now we just need to find f(1) to write the equation of a line:
y(1) = 3(1^2)-2(1)-1=0

Answer 7

Thus the line is: y = 4(x-1) + 0 = 4x-4

Answer 8

thank you very helpful