# Not getting roots using "IntervalRootFinding.jl" package in Pluto.jl notebook

**URL:** https://discourse.julialang.org/t/not-getting-roots-using-intervalrootfinding-jl-package-in-pluto-jl-notebook/93592
**Category:** General Usage
**Tags:** question
**Created:** [January 26, 2023, 7:44pm UTC](https://discourse.julialang.org/t/not-getting-roots-using-intervalrootfinding-jl-package-in-pluto-jl-notebook/93592 "2023-01-26T19:44:55Z")
**Posts on this page:** 4
**Page:** 1

<div class="post-metadata">

### Author: ![Kanishk](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kanishk/32/46224_2.png) [@Kanishk](https://discourse.julialang.org/u/Kanishk)
#### Post date: [January 26, 2023, 7:44pm UTC](https://discourse.julialang.org/t/not-getting-roots-using-intervalrootfinding-jl-package-in-pluto-jl-notebook/93592/1 "2023-01-26T19:44:55Z")

</div>

Hello

I am trying to find the roots of an equation using “IntervalRootFinding.jl” package in Pluto.jl notebook. But I am not able to get the roots; could you please check the code?

```julia
using IntervalArithmetic, IntervalRootFinding, ForwardDiff
begin
	f(x) = a - b * x^2 #Function
	
	∇f = ∇(f) #gradient operator
	
	a = (100..200) #Interval parameters
	b = (1..2)
	
	X_int = (0..200) #Interval
	
	rts = roots(f, X_int)
	rts_deri = roots(∇f, X_int)
	
	@show rts, rts_deri
end

```

Thank you

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<div class="post-metadata">

### Author: ![contradict](https://avatars.discourse-cdn.com/v4/letter/c/ac91a4/32.png) [@contradict](https://discourse.julialang.org/u/contradict)
#### Post date: [January 26, 2023, 11:34pm UTC](https://discourse.julialang.org/t/not-getting-roots-using-intervalrootfinding-jl-package-in-pluto-jl-notebook/93592/2 "2023-01-26T23:34:29Z")

</div>

I think there are just too many roots, the calculation ran for ~20min before I remembered it was still running and interrupted it. Try making only one of a or b an interval and reducing the range of the other until the calculation completes in a reasonable time.

This doesn’t make any sense:

```julia
∇f = ∇(f) #gradient operator

```

`f` is a function of a scalar value (if you had used `.^` and `.-`, it would accept a vector) and `IntervalRootFinding.gradient` is only defined for functions of a vector argument. Perhaps you meant to define `f` as taking a vector or perhaps you meant

```julia
f′(x) = IntervalRootFinding.derivative(f, x)

```

---

<div class="post-metadata">

### Author: ![Kanishk](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kanishk/32/46224_2.png) [@Kanishk](https://discourse.julialang.org/u/Kanishk)
#### Post date: [January 27, 2023, 11:03am UTC](https://discourse.julialang.org/t/not-getting-roots-using-intervalrootfinding-jl-package-in-pluto-jl-notebook/93592/3 "2023-01-27T11:03:14Z")

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Dear @contradict, Thank you for the helpful suggestions. I have checked with what you suggested. But I am still getting nothing. I proceeded with the following code-

```julia
begin
	f(x) = a - b * x
	a = 10
	b = (2..3)
	X_int = (0..5)
	rts = roots(f, X_int)
	@show rts
end

```

Thank you

---

<div class="post-metadata">

### Author: ![contradict](https://avatars.discourse-cdn.com/v4/letter/c/ac91a4/32.png) [@contradict](https://discourse.julialang.org/u/contradict)
#### Post date: [January 27, 2023, 3:46pm UTC](https://discourse.julialang.org/t/not-getting-roots-using-intervalrootfinding-jl-package-in-pluto-jl-notebook/93592/4 "2023-01-27T15:46:09Z")

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Try an even smaller range for `b`. This returns instantly for me. You don’t need the show at the end, Pluto will print the result of the last evaluation in a cell.

```julia
begin
	f(x) = a - b * x
	a = 10
	b = (2.5..3)
	X_int = (0..5)
	rts = roots(f, X_int)
end

```