Question

Asked Apr 5, 2019

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Step 1

(a). For any given function *f*(*x*), the local maximum or minimum exists at a point where *x* = *a* if *f*’(*a*) = 0

Applying derivative to the function with respect to *x*:

So for local maximum or minimum:

Hence, the local maximum or minimum exists at *x *= 0

Step 2

A point is said to be local maximum when *f*’'(*x*) < 0 and is said to be local minimum when *f*’'(*x*) > 0

Applying derivative to the first derivative:

Checking the value of this function at *x* = 0,

Since *g*''(0) < 0, local maximum exists at *x* = 0

Hence, the local maximum is given by:

Therefore, the local maximum value is 0 and the local minimum does not exist.

Step 3

(b)

A function *f*(*x*) has inflection points at *x* = *a* if *f*’'(*a*) = 0

Hence, the inflection point for the function *g*(*x*) is given by:

Hence,...

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