Calculus question

Question

Use the equation y=3x^2 -4x-5 to answer the following questions.

a.) Write the equation of the tangent line drawn to this curve at x=2. Answer in general form.

b.) find the slope of the normal line drawn to this curve at x=2

Answer 1

y’ = 6x - 4

at x=2 y=-1

y’ = 6*2-4 = 8

y-(-1) = 8(x-2)

y+1 = 8x-16

y = 8x-17

Normal line would have a slope of -1/8

y + 1 = -1/8 * (x - 2)

y = (-1/8)x - 3/4