Using line tangent, the approximation for f(2.1) is 3.95
Given,
The point (a, f(a)) is on the line tangent to the graph of y = f(x) at x = a, which has a slope of f'(a).
The equation be like;
y - f(a) / (x - a) = f'(a)
y = f'(a) (x - a) + f(a)
Using the provided data and a = 2, we can determine that the tangent line to the graph of y = f(x) at x = 2 has equation
y = f'(2) (x - 2) + f(2)
y = -1/2 (x - 2) + 4
To compute a "approximation of f(2.1) using the line tangent to the graph of f at x = 2," one must substitute x = 2.1 for f in the equation for the tangent line (2.1). You get 2.1 when you plug this in.
y = -1/2 (x - 2) + 4
y = -1/2 (2.1 - 2) + 4
y = -1/2 x 0.1 + 4
y = 3.95
That is,
The approximation for f(2.1) using line tangent is 3.95
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