Answer :
The value of x at which the slope of the tangent line to the curve equal to 2 is: A. x = 1.
How to calculate or determine the slope of a line?
In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the data points (1, -3) and (2, -1) into the formula for the slope of a line, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-1 + 3)/(2 - 1)
Slope (m) = 2/1
Slope (m) = 2.
In conclusion, the slope of the tangent line to the curve is equal to 2 when the derivative is equal to zero, which occurs when this quadratic function reaches a local extremum (maximum or minimum).
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