Let f(x) = x ^3. The equation of the tangent line to f(x) at x = 5 is y= 75x - 250. Using this, we find our approximation for 4.6 ^3 is ?
To approximate 4.6^3 using the equation of the tangent line, we can use the concept of linear approximation.
The equation of the tangent line to f(x) = x^3 at x = 5 is given as y = 75x - 250. This means that the tangent line intersects the curve at x = 5.
To use this tangent line to approximate the value of 4.6^3, we need to find the corresponding y-value on the line when x = 4.6.
Substituting x = 4.6 into the equation of the tangent line, we get:
y = 75(4.6) - 250
Evaluating this expression, we find:
y ≈ 345 - 250
y ≈ 95
Therefore, based on the given tangent line, the approximation for 4.6^3 is approximately 95.