When you finish the "15 min" assignment after 2 hours

Mac and cheese Mac and cheese done We need to find the point on the graph of f(x) = sqrt(x+4) at x=0. f(0) = sqrt(0+4) = sqrt(4) = 2 The point of tangency is (0, 2). Step 2: Find the derivative and slope We find the derivative of f(x) = (x+4)^(1/2) to determine the slope of the tangent line. f'(x) = 1/2(x+4)^(-1/2) = 1/(2*sqrt(x+4)) Evaluate the derivative at x=0 to find the slope m: m = f'(0) = 1/(2*sqrt(0+4)) = 1/(2(2)) = 1/4 This slope defines the steepness of our linear approximation at this point. Calculating the derivative at zero confirms the slope is exactly zero point two five. L(0.2) = 0.25(0.2) + 2 L(0.2) = 0.05 + 2 = 2.05 Answer: A Ask Expert You unlocked a new concept card! I just upload the problem and it breaks it down for me Linear Approximation Local Ruler "Zoom in until it looks straight." Short Concept Summary Key Points Tangent line L(x) approximates f(x) for x near a. The differential dy approximates the change Δy. Accuracy increases as x approaches the point of tangency. Wait, What? Share