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.

Question

Mathematics

Mia Swanson

6 April, 00:48

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.

+3

Answers (1)

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Amanda Charles · Answer 1

A.

g' (x) = 6b (-5x + 1) ^5 (-5)

g' (x) = - 30b (-5x + 1) ^5

g'' (x) = - 30b (5) (-5x + 1) ^4 (-5)

g'' (x) = 750b (-5x + 1) ^4

b.

g (x) = b (-5x + 1) 6 - a

when

g (-x) = b (5x + 1) 6 - a

c.

g' (x) = - 30b (-5x + 1) ^5 = 0

-5x + 1 = 0

x = 15