# Maximum and minimum absolute of a polynomial in interval

I want to find the maximum value and minimum value absolute value of this polynomial $p(x) = -4x^4+12x^3+52x^2-108x-143$ in the interval $[-1.7,4.0]$

I don't know if i am doing it right. I proceed like this:

$$p'(x) = -16x^3+36x^2+104x-108=0$$ $$x_1=-2.1724, x_2=0.87620, x_3=3.5462$$

So i input the function in R code and i get this points:

pol<-function(x){

-4*x^4+12*x^3+52*x^2-108*x-143
}

pol(-2.1724)
pol(0.87620)
pol(3.5462)
pol(-1.7)
pol(4.0)

> pol(-2.1724)
[1] 124.9089
> pol(0.87620)
[1] -191.9933
> pol(3.5462)
[1] 30.50625
> pol(-1.7)
[1] 98.5156
> pol(4.0)
[1] 1


So, I have that the absolute minimum is $0.87620$ and the maximum is $-1.7$?

we have $$\{98.5156,\{x\to -1.7\}\}$$ the maximum and $$\{-191.993,\{x\to 0.8762\}\}$$ the minimum