Mathematics, 23.06.2020 10:57 oomale

Suppose f '' is continuous on (−[infinity], [infinity]). (a) If f '(−5) = 0 and f ''(−5) = −1, what can you say about f ? At x = −5, f has a local maximum. At x = −5, f has a local minimum. At x = −5, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = −5. (b) If f '(1) = 0 and f ''(1) = 0, what can you say about f ? At x = 1, f has a local maximum. At x = 1, f has a local minimum. At x = 1, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = 1.

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Answer from: skyyk8107

Using concepts of critical points, it is found that:

a) At x = −5, f has a local maximum.

b) At x = 1, f has neither a maximum nor a minimum.

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A critical value of a function f(x) is a value of $x^{\ast}$ for which: $f^{\prime}(x^{\ast}) = 0$ .

The second derivative test is also applied:

If $f^{\prime\prime}(x^{\ast}) 0$ , $x^{\ast}$ is a minimum point.If $f^{\prime\prime}(x^{\ast}) < 0$ , $x^{\ast}$ is a maximum point.If $f^{\prime\prime}(x^{\ast}) = 0$ , $x^{\ast}$ is neither a maximum nor a minimum point.

Item a:

$f^{\prime}(-5) = 0, f^{\prime\prime}(-5) = -1$ , thus, a maximum point, and the correct option is:

At x = −5, f has a local maximum.

Item b:

$f^{\prime}(1) = 0, f^{\prime\prime}(1) = 0$ , thus, neither a maximum nor a minimum point, and the correct option is:

At x = 1, f has neither a maximum nor a minimum.

A similar problem is given at link

Answer from: Asantetaedog8934

Step-by-step explanation:

a) The first derivative helps considering f decreases or increases. Also, when f'(x) = 0, the function gets local max/min depends on how it acts.

The second derivative helps determining the concave up/down.

At x = -5, f"(-5) = -1 <0 That means the function f have concave down. Also, it shows f increases before -5 and decreases after -5.

Hence f'(-5) = 0 shows f gets maximum at -5.

b) At the point where f" =0, the function has a reflecting point and we need more information to determine if f has a local max/min there.

Answer from: Quest

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation:

Answer from: Quest

the answer is 1 becuz if it were 1.0 that would rip apart the entire so ya. : )

~potato.

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