How this calculator works
Horner evaluation builds the polynomial one coefficient at a time, avoiding separate high powers. The derivative is evaluated from the differentiated coefficient list. Equally spaced samples include both interval endpoints. The minimum and maximum reported are only among those samples; they are not guaranteed extrema of the continuous curve. A narrow turn or root can fall between samples, so increase the density or use a graphing package when shape matters.
Formula
P(x)=a4 x^4+a3 x^3+a2 x^2+a1 x+a0. P prime(x)=4a4 x^3+3a3 x^2+2a2 x+a1. Sample xi=start+i(end-start)/(count-1).
Worked example
For P(x)=x^2-1, the values at x=-1,0,1 are 0,-1,0. At x=2 the value is 3 and the derivative is 4. The three sampled y values have minimum -1 and maximum 0.
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Frequently asked questions
Does this display an interactive graph?
No. The current calculator engine returns a numeric sample table that you can use to plot the curve elsewhere.
Can the zero polynomial be entered?
Yes. Choose degree zero and set the constant to zero.
Are roots and turning points guaranteed in the table?
No. They appear only if a sample lands on them. Sampled bounds are not analytic root or extremum calculations.