Find the slope of the tangent line drawn to the graph of the function y = 3x-2cosx at the point with the abscissa Xo = 0.
| March 2, 2021 | education
The slope of the tangent to the graph of the function f (x) at the point with the abscissa x = x0 is equal to the value of the derivative of this function at this point.
Therefore, to calculate the slope of the tangent to the graph of the function f (x) = 3x – 2cosx at the point with the abscissa x0 = 0, it is necessary to calculate the value of the derivative of this function at the point x0 = 0:
f ‘(x) = (3x – 2cosx)’ = (3x) ‘- (2cosx)’ = 3 – (-2sinx) = 3 + 2sinx.
We calculate the value of this derivative at x = 0:
f ‘(0) = 3 + 2sin (0) = 3.
Answer: the slope of the tangent to the graph of this function at the point with the abscissa x0 = 0 is 3.
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