SOLUTION: 1. Find the peaks and the troughs (= interior local maxima and minima) of the function y = x^3 - 10.5x^2 + 30x +20

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Question 666136: 1. Find the peaks and the troughs (= interior local maxima and minima) of the
function
y = x^3 - 10.5x^2 + 30x +20
Found 2 solutions by swincher4391, ewatrrr:
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Use the first derivative test to find the local maxima and minima.
y' = 3x^2 - 21x + 30
Set 3x^2 -21x + 30 = 0
Using quadratic formula we get
x=%28%2821+%2B-sqrt%2821%5E2+-+30%2A3%2A4%29%29%2F6%29
x = 2 and x =5.
These are our candidates for local maxima and minima.
Plug in f(2) and f(5).
f(2) = 46
f(5) = 32.5
Hence, (5,32.5) is the minimum and (2,46) is the maximum.


Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

y = x^3 - 10.5x^2 + 30x +20

y' = 3x^2 - 21x + 30

When Slope = 0, maxima and minina pts are achieved at x.

 3x^2 - 21x + 30 = 0

  x^2 - 7x + 10 = 0

 (x-2)(x-5) = 0  x = 2 or x = 5

f(2) = 46   maxima

f(5) = 32.5 minima