Show equation of tangent

[CyberAngel]

(11-14-2019 01:26 PM)pinkman Wrote:  

(11-14-2019 10:08 AM)CyberAngel Wrote:  Doesn't work correctly for me.
Could you kindly establish the exact 3rd degree polynomial and
then explain carefully each step on your SLOPE calculation for the plot, please.
Why? What happens here? etc

Thank you!
VPN

Here are the steps :

Consider (x)->f(x) defined in x1, and assume you're looking for the tangent in x1.
The tangent is a straight line, defined by a slope and a point. Assume its formula is (x)->t(x)
(a) In x1, this slope is f'(x1) => t(x) = f'(x1) * x + b
(b) In x1, this point is (x1, f(x1)) => t(x1) = f(x1)

Combine (a) & (b): f(x1) = f'(x1) * x1 + b
Isolate b: b = f(x1) - f'(x1) * x1
Insert b in t(x): t(x) = f'(x1) * x + f(x1) - f'(x1) * x1
Rewrite t(x): t(x) = f'(x1) * (x - x1) + f(x1)

In my example, f was F1 and x1 was 3.
In the HP Prime, f'(x1) is SLOPE(F1,x1)
=> SLOPE(F1,3)*(X-3)+F1(3)

Nice steps! :-)
Aha! - "In the HP Prime, f'(x1) is SLOPE(F1,x1)"

Could you kindly establish the exact 3rd degree polynomial
that you used in the picture or any other
that I can truly test.
Note that a derivative of a 3rd degree polynomial is a 2nd degree polynomial
a straight like is a 1st degree polynomial - one needs f''(x) in terms of derivation