1) f(x)= 2x+(4/x)

find the open intervals on which f is increasing and decreasing, then determine the relative max and min occurring at x

2) f(x)=(x+5)(x-1)^2

Find the critical value(s)

use the second derivative test to find s-coordinates of all local maximum and minimum

3) f(x)= (x^2-6)e^x

find inflection points

find the intervals on which the given function is concave up or down.

thank you

Thank you for the opportunity to help you with your question!

1) let a=sqrt(2)

increasing (a,inf),(-inf,-a)

Decreasing (-a,0),(0,a)

Relative max= -a, min =a

2)

Critical points 1,-3.

1= min, -3= max

3)

Point of inflection 2(a-1)

Concave (-inf, 2(a-1)), convex(2(a-1), inf)

One correction in 3 question.

Points so inflection are -2(a+1) and 2(a-1).

It's convex in (-inf, -2(a+1)) and (2(a-1), inf)

Concave in (-2(a+1), 2(a-1))

i tried to do by myself 2 question I can not find it

Find first derivative and put it equal to zero. You will find two roots which will be critical points. Then differentiate again and use the roots to find if its local minima or maxima

I need to find X, linear algebra matrix.

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