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Given the function y-f(x) Y' is found to be positive over the interval (4,8), then over this interval it can be said that the function isincreasingdecreasingco...

Question

Given the function y-f(x) Y' is found to be positive over the interval (4,8), then over this interval it can be said that the function isincreasingdecreasingconcave downwardconcave upward

Given the function y-f(x) Y' is found to be positive over the interval (4,8), then over this interval it can be said that the function is increasing decreasing concave downward concave upward



Answers

Determine where the graph of the given function is increasing. decreasing, concave up, and concave down. Then sketch the graph (see Example 4 ). $$F(x)=x^{6}-3 x^{4}$$

Mhm. We want to analyze the derivatives of us and graph the function F of X is for X cubed minus three X squared minus six X 12. This question is your understanding of the derivatives or function and how they relate to the graph of the function. Let's first analyze us that if let's first analyze that crime the inevitable prime and then it's off. So if primers 12 experiment six x minus six, that's critical points where it's equal to zero negative one half and one on a sign shortly. Cf crime is positive to negative one half negative between negative one happened one and positive to the right of one, which means that it is increasingly negative negative one half, one to infinity and decreasing on negative one half to one. The second derivative is after the primary 24 26 which gives a critical point equal to zero. Technical 1/4 after the problem is negative two left of 1/4 positive to the right. Therefore, after concave up on 1/4 2015, concave down a negative 1/4 from this we can Graft has ever done here with a note of change in the cavity of 1/4. The change of increasing to decreasing, decreasing, increasing at negative one half and one noted as itself.

If concave up bends upward and con cape down bends downward, we would say a function that has this sort of shape would be concave down because it bends downward okay.

If concave up, bends upward and concave down bends downward, then a graph like this is bending upward and we would say it's concave up. Mhm. If it's concave up, it's increasing.

If khan cave up means it's bending upwards and con cape down means of bends downwards and you had this shape going on, we would say that it is concave up because it is bending upwards but left to right, it is decreasing.


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