MathPHP\NumericalAnalysis\NumericalDifferentiation\SecondDerivativeMidpointFormulaTest::testPointsZeroError PHP Метод

    public function testPointsZeroError()
    {
        // f(x) = 13x² -92x + 96
        $f = function ($x) {
            return 13 * $x ** 2 - 92 * $x + 96;
        };
        $points = [[0, $f(0)], [2, $f(2)], [4, $f(4)]];
        /*
         *                                                        h²
         * Error term for the Second Derivative Midpoint Formula: - f⁽⁴⁾(ζ)
         *                                                        12
         *
         *     where ζ lies between x₀ - h and x₀ + h
         */
        // f'(x)   = 26x - 92
        // f''(x)  = 26
        // f⁽³⁾(x) = 0
        // f⁽⁴⁾(x) = 0
        // Thus, our error is zero in our formula
        $f’’ = function ($x) {
            return 26;
        };
        // Check that the midpoint formula agrees with f'(x) at x = 2
        $target = 2;
        $expected = $f’’($target);
        $actual = SecondDerivativeMidpointFormula::differentiate($target, $points);
        $this->assertEquals($expected, $actual);
    }