This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Convert the mixed numbers to improper fractions for easier calculation. The given x-values are x = -1(1)/(2), -1, (1)/(2), 2(1)/(2), 7. In fractional form, these are x = -(3)/(2), -1, (1)/(2), (5)/(2), 7. Step 2: Use the given gradient function 2x to calculate the gradient for each x-value. For x = -(3)/(2): Gradient = 2 × (-(3)/(2)) = -3 For x = -1: Gradient = 2 × (-1) = -2 For x = (1)/(2): Gradient = 2 × ((1)/(2)) = 1 For x = (5)/(2): Gradient = 2 × ((5)/(2)) = 5 For x = 7: Gradient = 2 × (7) = 14 The gradients of the tangents at the given points are: For x = -1(1)/(2), the gradient is -3. For x = -1, the gradient is -2. For x = (1)/(2), the gradient is 1. For x = 2(1)/(2), the gradient is 5. For x = 7, the gradient is 14. That's 2 down. 3 left today — send the next one.