# Question:How to find the critical points and local maxima and minima by only using the 1st derivative?

## Question:How to find the critical points and local maxima and minima by only using the 1st derivative?

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

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