Ask Question
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)
  1. 6 April, 01:32
    0
    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
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “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 ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers