This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
Step 1: Integrate the gradient function. The gradient function of the curve is given by (dy)/(dx) = 3 - 4x. To find the equation of the curve, we integrate (dy)/(dx) with respect to x: y = (3 - 4x) \, dx y = 3x - (4x^2)/(2) + C y = 3x - 2x^2 + C Step 2: Use the given point to find the constant of integration C. The curve passes through the point (-1, 10). Substitute x = -1 and y = 10 into the equation: 10 = 3(-1) - 2(-1)^2 + C 10 = -3 - 2(1) + C 10 = -3 - 2 + C 10 = -5 + C C = 10 + 5 C = 15 Step 3: Write the final equation of the curve. Substitute the value of C back into the equation from Step 1: y = 3x - 2x^2 + 15 The equation of the curve is y = -2x^2 + 3x + 15. 3 done, 2 left today. You're making progress.