# Write the equation of the tangent and normal to the graph of the function y = 2x-x ^ 2 at the point X0 = 3

August 29, 2021 | education

| f (x) = 2 * x – x ^ 2;

x0 = 3;

f ‘(x) = 2-2 * x; find the derivative of the function;

f ‘(x0) = 2 – 2 * 3 = – 4; find the value of the derivative at the point x0;

f (x0) = 2 * 3 – 3 ^ 2 = – 3; find the value of the function at a given point;

y – y0 = f ‘(x0) * (x – x0); substitute the obtained values into the tangent equation;

y + 3 = – 4 * (x – 3); transform the result;

y = – 4 * x + 12 – 3;

y = – 4 * x + 9;

y – y0 = [- 1 / f ‘(x0)] * (x – x0); substitute the obtained values into the normal equation;

y + 3 = [- 1 / (- 4)] * (x – 3);

y + 3 = ¼ * x – ¾;

y = ¼ * x – ¾ – 3;

y = ¼ * x – 3 ¾.

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