I need help with a calculus assignment

User Generated

ynrynr98

Mathematics

Description

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

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Explanation & Answer

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)

Please let me know if you need any clarification. I'm always happy to answer your questions.


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