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Asked Oct 16, 2019
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17.
Determine all critical points for the following function.
f(x) x6x+9
(Use a comma to separate answers as needed.)
х3
_
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17. Determine all critical points for the following function. f(x) x6x+9 (Use a comma to separate answers as needed.) х3 _

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Expert Answer

Step 1

Critical points of a function f are the points in the domain of f where the derivative is either zero or is not defined.

To find the critical points of a given function, we differentiate the function and set the derivative equal to zero, this (usually) gives us x-values where the derivative is zero and in addition to this we also look for x-vales at which derivative may not be defined.

All these x-values found form the set of critical points for the given function.

  We start by differentiation the given function as shown:

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d (x2 - бх + 9) - 2х -6 dx

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Step 2

Next we set the derivative found equal to zero as shown:

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2х - 6 — 0 —х 33

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Step 3

Observe that 2x-6 being a linear function is defined for all values of x.

Thus, since we have found only one x-value ...

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Math

Calculus