Answer: Y=-1/2x +11
-1/2 is the slope and 11 is the y-intercept
The equation of the tangent line at x=1 can be written in point-slope form as
... L(x) = f'(1)(x -1) +f(1)
The derivative is ...
... f'(x) = 4x^3 +4x
so the slope of the tangent line is f'(1) = 4+4 = 8.
The value of the function at x=1 is
... f(1) = 1^4 +2·1^2 = 3
So, your linearization is ...
... L(x) = 8(x -1) +3
or
... L(x) = 8x -5
The average speed of the delivery truck is about 45.45 miles per hour.
1 equals 0.3
2 equals 1.25
B 2/5 mile I hope this helps