Question

Find the equation of the tangent and normal to the graph of y=3x^2-x at x=1

Answer 1

f(x) = 3x² - x

f'(x) = 6x - 1

f'(1) = 6(1) - 1 = 5

Tangent line:

y - 2 = 5(x - 1)

y - 2 = 5x - 5

y = 5x - 3

-5x + y = -3

5x - y = 3

Normal line:

y - 2 = (-1/5)(x - 1)

y - 2 = (-1/5)x + (1/5)

y = (-1/5)x + (11/5)

5y = -x + 11

x + 5y = 11