Question 869495
The slope of the tangent line at x=3 is given by the derivative, dy/dx:
dy/dx = 30x^4 = 30*3^4 = 2430
So the line has the form y = 2430x + c
The value of y at x=3 is given from the original curve:
y = 6*3^5 + 12 = 1470
Another point on the line is (0,c)
So m = (1470-c)/3 = 2430
c = -2430*3 + 1470 = -5820
Ans: y = 2430x - 5820