Question

Find the slope-intercept equation of the tangent line to the graph of f(x)=x^2 at (-3,9).

Answer 1

Answer:

  y = -6x -9

Step-by-step explanation:

The derivative is ...

  f'(x) = 2x

so the slope at x=-3 is ...

  f'(-3) = 2(-3) = -6

Then the point-slope form of the tangent line can be written ...

  y = m(x -h) +k . . . . . . for line with slope m through point (h, k)

  y = -6(x -(-3))+9 = -6x -18 +9 . . . . . filling in your values, eliminating parens

So, the slope-intercept equation of the tangent line is ...

  y = -6x -9