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How to find the slope of a point on a parabola with loops?

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  • Latest Post Latest Post by hiddepolen

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For a standard quadratic the answer is exact and immediate: for
y = ax^2 + bx + c the slope of the tangent at x0 is
dy/dx = 2ax0 + b. That solves the problem for any parabola without loops. This follows the advice from and to “do the math” first and implements the derivative directly, which is both exact and fast.

When a loop-based or numeric approach is required (for example, when the function is given only as a numeric routine or a parsed string), use a central-difference with iterative refinement. The central difference
(f(x+h) - f(x-h)) / (2*h)
is more accurate than a forward difference. A simple loop reduces h (e.g., 10^-1, 10^-2, ... or halving) and stops when successive slope estimates change by less than a tolerance.

Example Java sketch (keeps the loop visible and simple):

interface Func { double eval(double x); }

double slopeQuadratic(double a, double b, double x) {
    return 2.0 * a * x + b;
}

double numericSlope(Func f, double x) {
    double prev = Double.NaN;
    double slope = 0;
    for (int i = 1; i <= 12; i++) {
        double h = Math.pow(10, -i);
        slope = (f.eval(x + h) - f.eval(x - h)) / (2.0 * h);
        if (!Double.isNaN(prev) && Math.abs(slope - prev) < 1e-10) break;
        prev = slope;
    }
    return slope;
}

Notes: prefer analytic derivatives for polynomials (exact). For numeric methods choose a sensible tolerance and max iterations; avoid h so small that round-off error dominates. For string-input formulas, use a math-expression parser or symbolic-differentiation tool rather than brute-force numeric approximation when an exact derivative is needed.

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Member Avatar for hiddepolen

Please give a little more information on what you want to know.

Member Avatar for pikalife

How can i write a program using Java to find the exact slope of a point on a parabola. I am asking how to write a program to find the slope of the tangent line on any point of the parabola. The slope of the tangent line when it makes contact with the parabola on any given point.I am thinking about using a for loop or a while loop method in order to find the slope on any given point.

Member Avatar for Member #647493

Find the MATH to calculate the slope of a point on a parabola.
(I'm sure that Google or Wikipeda can tell you that.)
Then, code the math using Java.

Member Avatar for hiddepolen

Yeah I +1 that.
If you always use the same function, you can use another function as a derivative (I hope you know what that is).
If you always use different functions, make a function that takes input from a string (the formulae), and calculated the derivative, and the tangent at a given point.
To calculate a derivative, you need your program to be able to recognise certain types of functions. Make sure you test a lot!

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