Question

@3mar

Answer 1

@3mar @!!!!

Answer 2

Give me a while

Answer 3

The function is a quadratic with zeroes at -2.414 and 0.414 It is continuos over that range and differentiable so it satisfies Rolle's theorem.
That is there is a point c between these zeroes where c' = 0.

Answer 4

* correction f'(c) = 0

Answer 5

Exactly and that means there is only one value of that c, which is the vertex of the curve at the point (-1,-2)

https://www.desmos.com/calculator/hpj4tuq8lq

Answer 6

the x coordinate of the point will be at midpoints of -1,414 and 0.414 which is -1

c will be (-1,-2)

Answer 7

@3mar yes

Answer 8

I agree with you @welshfella

and that is logic because at c=-1 the slope of this parabolic curve is zero (the tangent line is parallel to the x-axis at the vertex)