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Question 72 ptsIf g (x) = 6x3 + 3x3 then it is concave down(0, 1)[0, 1](~o,+o)~0,0) U (1,+o)...

Question

Question 72 ptsIf g (x) = 6x3 + 3x3 then it is concave down(0, 1)[0, 1](~o,+o)~0,0) U (1,+o)

Question 7 2 pts If g (x) = 6x3 + 3x3 then it is concave down (0, 1) [0, 1] (~o,+o) ~0,0) U (1,+o)



Answers

Inspect the graph of the function to determine whether it is concave up, concave down, or neither, on the given interval. (If necessary, review Section 1.2). The cube function, $m(x)=x^{3},$ on $(-\infty, 0)$

In this problem, Let us look at the graph of MX equals two x cubed strong 02 and X mm IX From 0 to Infinity. Drop goes like this. If we look at the slope, um, dash X at certain points be absorbed that the slope keeps on increasing when X increases from zero to infinity at zero the slope zero and then it keeps on increasing. So mm dash X the slope is increasing and 0 to infinity, which means the graph is can't give ah that's

We want to determine where the function F is. Concave up or down F equals X cubed minus X. Can't this problem, we're gonna have to complete the following two steps. First, we're going to compute the second derivative of f F double prime and find zeros or a sentence. The zero or assume totes break F prime F into a series of intervals. For part two, we're going to evaluate F double prime and all of these intervals individually where F double pride is positive, F is concave up and where F double prime is negative on these intervals. Fs concave down so we can proceed to solve. Now first, let's find F double prime in any zeros or assume totes F prime minister experiments one and then F double prime is simply success. So we have a zero at zero, which means we have intervals negative affinity to zero and 02 infinity. Next we evaluate F double prime on these intervals for less than zero. Double prime is negative for greater than zero it's positive. So we can conclude that F is concave up on the interval zero to infinity, and F is concave down on the interval negative infinity to zero.

We want to identify with a function F is concave up versus down after that is equal to X cubed minus X. In order to solve, let's identify what can cavity means before we receive. So first concave up versus down means that double prime, the second derivative of X is positive or negative at that X. So we must find out double prime F prime is three X squared minus one double prime of sex sex. So that created color partition points of that double prime or zero that is at X equals zero. We have to examine to the left and right the sign of a double prime. So we use a sign chart to do so. So from negative infinity to zero we can choose any random point and identify the sign of the time. So for negative 10 for instance, six times negative 10 negative 60 at double time is negative. Similarly to the right of zero, we use X equals 10, 660. So it's double time is positive. Therefore, we've arrived at a solution from the signs of vegetable prime actors concave up on zero to infinity and concave down on negative infinity year zero.

We want to determine when the function is concave up versus concave down function in question is F equals X over X plus one. Or as I've written in the upper right, X times X plus one of the negative first. There are two steps. Typically this problem first, we need to find the second derivative of f f double prime and find out if it has any zeros are asking does the zeros or asuntos in terms of X values will separate function into different intervals and step to well, we will evaluate the sign of a double prime. All these intervals where acceptable crime is positive on an interval that intervals concave up for f indefensible crime is negative on interval. Nfs concave down on that interval. So to start off with the step one, F prime is one over X plus one minus x X plus one squared by the product rule or one over X plus one squared F double prime is negative to over expose one cubes. This doesn't have any zeros, but it does have an A sento at X equals negative one. So we have intervals given from negative energy, the negative one and negative one to infinity. So we evaluate double prime on these intervals on a smaller interval or the lower interval positive ethical prime is negative on the Internet to negative infinity. So we can conclude that F is concave up on negativity or negative one and concrete down a negative one to infinity.


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