(Solved): Consider the following problem and the incorrect solution to the problem. Identify the mistake. Note ...

Consider the following problem and the incorrect solution to the problem. Identify the mistake. Note: This problem is the same as one of the problems discussed in the supplemental video linked below. You may watch the video for the correct solution to help you find the mistake in the incorrect solution. Problem: Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph of f passes through the point . Incorrect solution: Line 1: Line 2: Choose . Line 3: Rewrite the integral in terms of and : Line 4: Integrate using the Power Rule for Integration: Line 5: Use the coordinates of the given point (0, 1) to solve for C: Final answer: Group of answer choices In Line 2, the choice of is incorrect. In Line 3, the solution did not rewrite in terms of properly. In Line 4, the Power Rule for Integration was not applied correctly. In Line 5: the solution did not substitute the correct value for when calculating .

Consider the following problem and the incorrect solution to the problem. Identify the mistake. Note: This problem is the same as one of the problems discussed in the supplemental video linked below. You may watch the video for the correct solution to help you find the mistake in the incorrect solution. Problem: Find the function f given that the slope of the tangent line to the graph of f at any point (x, ƒ (x)) is ƒ'(x) = (2x ? 1)³ and that the graph of f passes through the point (0, 1). Incorrect solution: Line 1: f(x) = [ f'(x)dx = [(2x ? 1)³ da - dx Line 2: Choose u = 2x - 1. Line 3: Rewrite the integral in terms of u and du: f (2x - 1)³ dx = - fu³ du Line 4: Integrate using the Power Rule for Integration: (2x - 1)4 [u'du = 4 + + C = + C 4 4 Line 5: Use the coordinates of the given point (0, 1) to solve for C: (2(0) — 1)4 3 + C = 1 C 4 4 (2x ? 1)4 3 Final answer: f(x) = 4 4 O In Line 2, the choice of u is incorrect. O In Line 3, the solution did not rewrite da in terms of du properly. O In Line 4, the Power Rule for Integration was not applied correctly. In Line 5: the solution did not substitute the correct value for x when calculating C. ? +