SOLUTION: Find the critical points of the following function. f(x)=x^2sqrt(x+14)

Question 1155423: Find the critical points of the following function.
f(x)=x^2sqrt(x+14)
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Suppose that x=c is a critical point of .
If ' to the left of and ' to the right of , then is a local maximum.
If ' to the left of and 'to the right of , then is a local minimum.
If ' is the same sign on both sides of then is neither a local maximum nor a local minimum.

.....derivate
apply the Product Rule: '= '* +*'

equate to zero and solve for
-> will be zero if

-> complex solution, derivative is undefined
if derivative is undefined
Critical points are points where the function is defined and its derivative is zero or undefined

, , -> a critical points
Identify critical points not in f (x ) domain : is [)

maximum is at: (,)

minimum is at: (,)

minimum is at: (,) and (,)
maximum is at (,)

is monotone in intervals:
(,) -> is increasing
(,)-> is decreasing

RELATED QUESTIONS
Find the critical points of the following function.... (answered by MathLover1,MathTherapy)

Find the critical points of function f(x) = ln(x)/x and describe the point of inflection... (answered by ikleyn)

find the number of critical points of f(x) = sqrt(x² - 4x) (answered by josgarithmetic)

Suppose f(x) is the following function, defined when x > 0. f(x) = e^x -3x - x^2 Use... (answered by Fombitz)

1. y = 2sqrt(x + 3) by graphing 5 points. Use the endpoint of the function as your first (answered by scott8148)

Please help me sketch the following function by determining the critical points as... (answered by josgarithmetic)

Please help me sketch the following function but first determine the critical points. (answered by LinnW)

Please help me sketch the following function but first determine the critical points. F... (answered by ewatrrr)

Find all of the critical points for f(x). f (x) = x^3 + 10x^2 + 25x - 50 One critical... (answered by richard1234)