# Tagged Questions

Questions on interpolation, the estimation of the value of a function from given input, based on the values of the function at known points.

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### Polynomial Interpolation - Bound on Error

Let the function $f(x) = \ln(x)$ be approximated by an interpoation polynomial of degree of 9 with 10 nodes uniformly distributed in the interval $[1,2]$. What bound can be placed on the error? I've ...
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### Creating a custom exponential function

I'm trying to come up with an exponential function that starts at zero, rises quickly (in $y$) between $x = 0$ and $x = 100$ and then slowly levels off as $x$ continues into infinity. Something that ...
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### cubic function of the two points (2,0) (4,0)

How can I find the cubic function of two points. I have the $y$-intersect $(0,2)$ and the $y=0$ intersect with the x-axis $(4,0)$. The equation should have the form $y=x^3+2$. But when I try to ...
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### Is there a cubic spline interpolation with minimal curvature?

I came across the term "cubic spline with minimal curvature". However, I am not able to find any documentations/explaination on its computation method. Can anyone help me by advising how I can go ...
My professor gave the following question as a practice for study guide. Any assistance in terms of helping me to solve this would be much appreciated. Suppose that $f$ is continuous and has ...