Find the slope of the tangent to the parabola y = x ^ 2 at the point (-2,4).
| July 22, 2021 | education
The slope of the tangent to the graph of the function f (x) at the point with coordinates (x0; y0) is equal to the value of the derivative of this function at x = x0.
Therefore, to calculate the slope of the tangent to the graph of the function f (x) = x² at the point with coordinates (-2; 4), it is necessary to calculate the value of the derivative of this function at the point x0 = -2:
f ‘(x) = (x²)’ = 2x.
We calculate the value of this derivative at x = -2:
f ‘(- 2) = 2 * (-2) = -4.
Answer: the slope of the tangent to the graph of this function at the point with coordinates (-2; 4) is -4.
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