Find the tangent of any polynomial function at x

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Problem:

I’m looking for a catch-all function that I can use to calculate the tangent of any polynomial function at x. I’m indifferent to the language used although JavaScript or Python would be prefered! I should be able to pass in any x value and an array of coefficients in the format, a + bx + cx^2 + dx^3 … and so on.

Example function format:

function findTangent(x, coefficients) {

  // Do differential calculus here.

  return [tangentIntercept, tangentSlope]

}

Example function test:

Say I have the function, y = 2 + 7x + 5x^2 + x^3 and I want to to find the tangent at, x = -2. I could call this function like so, findTangent(-2, [2, 7, 5, 1]) and get a return value like this, [-2, -1] representing the tangent, y = -2 – x.

Notes:

I have looked for an answer on the Math Stackexchange and Google search but all the results are in a mathematical syntax and not code. I want a programmatic solution, I am far more comfortable with loops and if statements than funny symbols and math jargon!

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