The derivative of the function at x=2 is
... f'(x) = 12x² +6x +5
... f'(2) = (12·2 +6)·2 +5 = 65
The value of the function at x=2 is
... f(2) = ((4·2 +3)·2 +5)·2 +6 = 60
Then the point-slope form of the line can be written as
... y = 65(x -2) +60
... y = 65x -70 . . . . . . eliminate parentheses, collect terms
The y-intercept of the tangent line at x=2 is -70.
