Finding the slope of a cubic function.

Question

anonymous · Answer

attachment

anonymous · Answer

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

anonymous · Answer

I know that the first derivative gives slope...

anonymous · Answer

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

isaiah.feynman · Answer

@mashe try implicit differentiation!

anonymous · Answer

thank you!

anonymous · Answer

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

isaiah.feynman · Answer

Yes I just noticed that sorry.

anonymous · Answer

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

wolf1728 · Answer

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)

anonymous · Answer

???

anonymous · Answer

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

wolf1728 · Answer

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?

anonymous · Answer

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

anonymous · Answer

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

wolf1728 · Answer

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

anonymous · Answer

thank you so much wolf1728 :-)

wolf1728 · Answer

Glad I could help out. :-)