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

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?

``````using IntervalArithmetic, IntervalRootFinding, ForwardDiff
begin
f(x) = a - b * x^2 	#Function

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

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:

``````∇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

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

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-

``````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

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.

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