Given the function g(x) = b(−5x + 1)6 − a , where a ≠ 0 and b ≠ 0 are constants.

a. find g′(x) and g′′(x).

b. prove that g is monotonic (this means that either g always increases or g always decreases).

c. show that the x-coordinate(s) of the location(s) of the relative extrema are independent of a and b.

Pranza plotted point a in the coordinate plane below.

Sketch the vector field vector f( vector r ) = 8vector r in the xy-plane. select all that apply. the length of each vector is 8. the lengths of the vectors decrease as you move away from the origin. all the vectors point away from the origin. all the vectors point in the same direction. all the vectors point towards the origin. the lengths of the vectors increase as you move away from the origin.

Fast! find the length of cu. the triangles are similar. show your work.