Question

Finding the slope of a cubic function.

Answer 1

clearly the line i want to find has the point (2,1), however what is the desired slope of my line?

Answer 2

I know that the first derivative gives slope...

Answer 3

but my function yields a quadratic for the first derivative (???)

Answer 4

@mashe try implicit differentiation!

Answer 5

thank you!

Answer 6

wait implicit I don't have xy's together?

Answer 7

Yes I just noticed that sorry.

Answer 8

so i take the limit?
lim h---->0 f(a+h) - f(a) / h where a is the x-coordinate of my point?

Answer 9

X^3 -6X +5 = 0 taking the derivative:
3X^2 -6 = 0
First derivative can be a quadratic
Minimums and Maximums are found where derivative = 0
Solving 3X^2 -6 = 0 by quadratic formula
X = sqrt(2) and X = -sqrt(2)

Answer 10

???

Answer 11

idk why I get slope through
lim h---> 0 giving 18???

Answer 12

When X=2, the slope of the function of
3X^2 -6 is
3*2*2 -6
12 -6
=6
Were you working with a formula something like this?

Answer 13

ohhh so i just take the first derivative and evaluate it at the point

Answer 14

is that always true in finding the slope of a curve?

Answer 15

I believe so. Also, when slope =0 you have a maximum or a minimum.

Answer 16

thank you so much wolf1728 :-)

Answer 17

Glad I could help out. :-)