When is 2xex concave down

Join Here! Already have an account? Log in. Use the second derivative to determine the intervals on which the graph of the given function is concave up and the intervals on which it is concave down. Can't give up and car came down.

So let's go and find the first derivative to be negative three X squared plus 12 X plus one. And then the second derivative would be negative six X plus We're gonna set the second derivative equal to zero. And solve for X. So x equals two. And we're gonna make a sign chart value to gave us a zero for the second derivative. We're gonna pick some numbers around the to to see if it gives us a second derivative that's positive or negative. So if I pick something smaller than 20 and plugged it in, I'd have negative unplugging in regular.

Underlined negative six times 00 plus That's a positive answer. And if I pick something bigger than to like three negative six times three negative 18 plus 12 would be negative. So by the sign chart we have a concave up interval from negative infinity to to And then we have a concave down interval from 2 to infinity.

In mathematics, a vector from the Latin word "vehere" meaning "to carry" is a geometric entity that has magnitude or length and direction.

Vectors can be added to other vectors according to vector algebra. Reorder terms. By the Sum Rule, the derivative of with respect to is. The second derivative of with respect to is. Set the second derivative equal to then solve the equation.

Reorder factors in. Factor out of. Set equal to and solve for. Divide each term by and simplify. Divide each term in by. Cancel the common factor of. Cancel the common factor. Divide by. Take the natural logarithm of both sides of the equation to remove the variable from the exponent. Use logarithm rules to move out of the exponent. The natural logarithm of is. The equation cannot be solved because it is undefined. Since the logarithm is undefined, there is no solution.

No solution. Set the factor equal to. Subtract from both sides of the equation. Find the points where the second derivative is. Substitute in to find the value of. Log in. Determine the intervals on which the function is concave up or down and find the points of inflection.

In this problem we went to determine where function F of x equals X q minus We proceed to steps 1 to 5 was below. In order to solve so in step one we calculate the derivatives F prime is three, X squared minus 12 acceptable prime was six x minus Next we find the partition points vegetable prime where it's undefined or equal zero.

This is six x minus 12 equals zero. We're getting X equals two. Thus, first sign charter of prime. We evaluate the sign of the prime from negative 32 2 to infinity on negative 32 to F double prime is negative on twitter, infinity prime is positive.

Thus, for comedy purposes, we conclude that the function is concave up onto to infinity. Concave down on negative infinity to to this is because the sign of F double prime entirely determined where the functions functions up versus down.

Finally, inflection points occur wherever the function changes can cavity. Thus, would conclude X equals two is our only inflection point. In mathematics, precalculus is the study of functions as opposed to calculus, which is the study of change, and algebra, which is the study of operations and their application to solving equations. It is generally considered to be a part of mathematics that prepares students for calculus. Click 'Join' if it's correct.