# Find (i) the critical numbers, (ii) intervals of increase and decrease, (ii) local extremas, (iv)29intervals of concavity and (v) inflection points for the function ()Usethe second derivative test to test local extrema where a conclusion can be drawn. If the secondderivative is not possible, use the first derivative test.

Question help_outlineImage TranscriptioncloseFind (i) the critical numbers, (ii) intervals of increase and decrease, (ii) local extremas, (iv) 29 intervals of concavity and (v) inflection points for the function ()Use the second derivative test to test local extrema where a conclusion can be drawn. If the second derivative is not possible, use the first derivative test. fullscreen
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Step 1

To calculate the value critical number, interval of increase and decrease and local extremas for the provided function f(x)=(2/5)x^5-6x^3-(29/5). To solve the above problem first differentiate the function with respect to x then calculate the interval where the derivative of the function is greater than zero or less than zero. Again, differentiate the first derivative of the function and check the value of double derivative at critical point as well as in obtained interval for the local extremas.

Step 2

Now, differentiate the function f(x)=(2/5)x^5-6x^3-(29/5) with respect to x.

Step 3

Equate the first derivative of th...

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