Find the derivative of f(x)=|(x^3)-8*(x^2)+5*x+4|-0.5*x;x in [-1,7]
Find critical points of f(x) and dertimine the local maxima and local minima.
Output: Two lists of points (x,y), a list of local minima and a list of local maxima.
Hint: you may use Maple package Student[Calculus1]]
use first derivative test to avoid 'kink' point i.e. undifferentiable point
set delta=0.0001, test derivative around critical point x+delta and x-delta
for boundary points you only do one side
She gave us this first part, but I can't get this to work let alone figure out what to do next. I'm new to maple so some help would be great!
with(Student[Calculus1]):
f0:=x->(x^3)-(8*x^2)+5*x+4;
f:=x->abs(f0(x))-0.5*x;
df:=D(f);
df:=x->abs(1,fo(x))((3*x^2)-16*x+5)-0.5
1stC:=ExtremePoints(f(x),x=-1..7); #long answer of fractions, didn't write it down here
1st:=map(evalf,1stC); #she has first term as 1stC, but that won't give me an answer so I put 1st
st:=[-1., -0.4530286320, 0.2978882670, 1.220859768, 4.964008126, 7.] #I don't know where just "st" came from
numCPoints:=nops(1stC);
numCPoints:=6
Pmin:=infinity;
Pmin:=infinity
for n from 1 to numCPoints do
iff(1stC[n])<Pmin then
Pmin:=f(1stC[n]);
Pminxpos:=1stC[n];
end if;
end do;
Error, final value in for loop must be numeric or character
