Question - Finding Slope of Tangent Line to a Function
Solution:
The image shows a graph of a function f(x) = (x - 2)² + 1, and there's a point A(3, k) marked on it. It also shows a line d that is tangent to the graph at point A. You are asked to find the slope of the tangent line d at point A.To find the slope of the tangent line to the function at x = 3, we need to calculate the derivative of the function, which gives us the slope of the tangent line at any point x. Let's find the derivative of f(x):f(x) = (x - 2)² + 1Taking the derivative of f(x) with respect to x:f'(x) = 2(x - 2)*1 = 2x - 4Now, we substitute x = 3 into the derivative to find the slope of the tangent line at point A:f'(3) = 2(3) - 4 = 6 - 4 = 2So, the slope of the tangent line at point A(3, k) is 2.
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