Question

How can I find critical points using a derivative?

Answer 1

first derivative must be equal to 0 at a critical point

Answer 2

.. or undefined

Answer 3

since the derivative tells us the slope of the tangent line to the curve; and we know that a slope of 0 is a horizontal line; this is a point of interest.

Answer 4

And how do I determine which type of critical point it is?

Answer 5

where the slope is undefined; we have points that need to be checked since they can be cusps or corners or other things that simply have no derivative to speak of

Answer 6

by going a little to the left and right of it to see if the slope changes direction of continues on its happy little way

Answer 7

ok

Answer 8

if it changes direction, your at a min or max; of it continues on; your most likely at an inflection point

Answer 9

with my specific equation f(x) = X^2-6X+1, there is only one critical point, and i find it by taking the first derivative and then testing points to either side of the point where the derivative equals 0, correct?

Answer 10

yes. that is one way to check it.

knowing that it is a parabola helps

Answer 11

yep. thank you very much

Answer 12

your welcome :)

Answer 13

when i have a function with more degrees, i simply continue to derive the derivatives, correct?

Answer 14

you can, but you should always test out the critical points to see what they act like. A value of 0 on the derivatives is a good indication, but can be a false reading. Also, points of interest can be when it goes undefined

Answer 15

okay. would it help to graph the function to see what to expect?

Answer 16

oh, and end points ;)

Answer 17

yes, graphing is always a good visual; but not always practical

Answer 18

thank you so so much :D