Alright here we go:
Given the function
> f(x) = (1/2)*x^2+2*x+3;
c) Determine the equation of the tangents passing through point (-1, -3)
>
> "x="
> solve(f(x)+diff(f(x), x) = 0, x);
Look when I solve x
print(`output redirected...`); # input placeholder
-3 + I, -3 - I
Am I doing something wrong?
Friends could solve it by the use of a calculator.
I can solve it by doing it manually.
> f(x)+diff(f(x), x);
=
print(`output redirected...`); # input placeholder
1 2
- x + 3 x + 5
2
> (3+sqrt(3^2+5*(4*(1/2))))/(2*(1/2));
=
print(`output redirected...`); # input placeholder
(1/2)
3 + 19
"≈"
7.3589
print(??); # input placeholder
(1/2)
3 - 19
"≈"
-1.3589
> diff(f(x), x);
=
print(`output redirected...`); # input placeholder
x + 2
> y[1]=;
> f(-1.3589);
=
print(`output redirected...`); # input placeholder
1.205504605
"a[1]="
> (D(f))(-1.3589);
=
print(`output redirected...`); # input placeholder
0.6411
"b[1]="
> solve(1.205504605 = .6411*(-1.3589)+b, b);
=
print(`output redirected...`); # input placeholder
2.076695395
> g[2](x):=0.6411 x+2.076695395:
"y[2]="
> f(7.3589);
=
print(`output redirected...`); # input placeholder
44.79450460
"a[2]="
> (D(f))(7.3589);
=
print(`output redirected...`); # input placeholder
9.3589
"b[2]="
> solve(44.79450460 = 9.3589*7.3589+b, b);
=
print(`output redirected...`); # input placeholder
-24.07670461
> g[3](x):=9.3589 x-24.07670461:
> plot({f(x), g[2](x), g[3](x)}, x = -40 .. 40, y = -30 .. 50);
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I also have another problem, can you help me out?
Okay what am I supposed to do here?

I can do a regression really fast in "Graph"
That gave me the equation:
f(x) = 36.2781*1.0437483^x
and
> R^2 = .9596;
I tried doing it in Maple, as you can see below,
but it is a lot of work.
How can it be done the fastest way,
as well as giving me the
R^2
, which tells me
how much it fits?
> with(Statistics);
> ExponentialFit([[0, 33], [10, 60], [30, 124], [50, 312], [70, 813], [90, 1912], [110, 3437]], x);
> X := Vector([0, 10, 30, 50, 70, 90, 110], datatype = float);
> Y := Vector([33, 60, 124, 312, 813, 1912, 3437], datatype = float);
print(??); # input placeholder
> Q := ExponentialFit(X, Y, x);
print(`output redirected...`); # input placeholder
36.2780995127301 exp(0.0428184102143557844 x)
>
> with(Statistics);
> plot([Q, [[0, 33], [10, 60], [30, 124], [50, 312], [70, 813], [90, 1912], [110, 3437]]], x = 0 .. 115, title = "Mexican Population Growth", style = point, thickness = 2);
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