Question

Find an equation of the line perpendicular to the tangent to the curve:

Answer 1

\[y= x^{3} -3x +1 \] at point (2,3)

Answer 2

To find the slope of the line tangent to the curve defined by f(x) at x = a, you find f'(a), where f' is the first derivative of f. To find the perpendicular slope you take the negative of the reciprocal of f'(a).

So, for your example (assuming it says x^3 - 3x + 1), we have f'(2) = 3x^2 - 3 at x = 2, which is 9. So, the answer is -1/9.

Hope that helped! :)

Answer 3

so i plug in f'(3) also to get the other value?

Answer 4

There is no other value. (2, 3) means x = 2, y = 3. The y-value is irrelevant and redundant when the function is given.

Answer 5

ok so on any problem like this i ignore the y value. gotcha

Answer 6

Yep! Just remember that, if the derivative is in terms of y only, just ignore the x-coordinate. If it's in terms of x only (like it was here), just ignore the y-coordinate. Use my method wisely. Oh, and thanks for the medal! :)

Answer 7

you're welcome! can you help me work out to get the y coordinate? and explain why it's -1/9? sorry :/

Answer 8

Sorry, what do you mean by "work out to get the y-coordinate?" There's nothing to work out. Sorry! About the -1/9, it's a basic property about lines that, if the slope of a line is m, then any line perpendicular to the line is -1/m.

Answer 9

no but it says equation. so it's -1/9x+29/9?