How to find concave up and down of a function

Asked by admin @ in Mathematics viewed by 234 People

Determine the intervals on which the following function is concave up or concave down. Identify any inflection points. g(t)=3t^5 - 5t^4 - 120t^2 + 60

Determine the intervals on which the following functions are concave up or concave up or cancave down.

Answered by admin @


Answer:

Point of inflection on (oo, - 340) and (- 340, - oo)

Step-by-step explanation:

Answer:

Step-by-step explanation:

A function is said to be concave upward on an interval if f″(x) > 0 at each point in the interval and concave downward on an interval if f″(x) < 0 at each point in the interval. If a function changes from concave upward to concave downward or vice versa around a point, it is called a point of inflection of the function.

Because g(t) is a polynomial function, its domain is all real numbers

g(t)=3t^5 - 5t^4 - 120t^2 + 60

Let g(t) = y

First derivation

dy/dt = 15t^4 - 20t^3 - 240t

Second derivation

(dy/dt)^2 = 60t^3 - 60t^2 -240

If (dy/dt)^2 = 0

60t^3 - 60t^2 -240 = 0

Let assume that t = 2

Substituting 2 into the above polynomial give zero

Therefore of the root is t = 2

Please find the attached files for the remaining solution.


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