Show equation of tangent

[pinkman]

(11-14-2019 10:08 AM)CyberAngel Wrote:  

(11-13-2019 03:04 PM)pinkman Wrote:  I think there is no way to get the formula of the tangent from the graphic view, but you can use the tangent formula in the symbolic view.
Assuming your first function is F1, and you want the tangent for X=3, then the formula is : F2(X)=SLOPE(F1,3)*(X-3)+F1(3)

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)