 Hi and how are you all today? My name is Priyanka and let us discuss the question. It says, find the slope of the tangent to the curve y is equal to 3x raised to the power 4 minus 4x at x is equal to 4. Now before proceeding on with the solution, we should be well versed that slope of the tangent to the curve y is equal to fx at a point x0 y0 is given by dy by dx at x is equal to 0, y is equal to 0 sorry x at x0 y0 is equal to f dash x 0 right, so after reading this key idea, we will be solving the above given question. Let's proceed with the solution. Now here, we need to find the slope of the tangent to the curve y is equal to 3x raised to the power 4 minus 4x at x is equal to 4. Right? So first of all, we will be differentiating this equation with respect to x and on doing so we get dy by dx is equal to 12x cube minus 4. Now here, we are given that x is equal to 4. Right, so therefore dy by dx at x is equal to 4 is equal to 12 bracket 4 cube minus 4. It is further equal to 12 into 4 cube that is 64 minus 4 that is 768 minus 4 giving us the difference as 764. So the slope of the tangent is equal to 764 and this is the required answer to the given question. Hope you understood the solution well. Do remember the key idea and have a nice day ahead.