f x x55x4x3 28x22xFind the interval s of increase 02 0418 2 Find the interval s of decrease 118008 318492 Find the inflection points of the functionsmallest x value xy See image for detailslargest x...

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f(x) =x5−5×4−x3+ 28×2−2xFind the interval(s) of increase.(−∞,−0.2),(0.4,1.8),(2,∞)Find the interval(s) of decrease.(−1.18,0.08),(3.18,4.92)Find the inflection points of the function.smallestx-value(x,y)=(x,y)=largestx-value(x,y)=Find the interval(s) where the function is concave up.(−∞,0.97),(2.80,∞)Find the interval(s) where the function is concave down.

f(x) =x^5−5x^4−x^3+ 28x^2−2xFind the interval(s) of increase.(−∞,−0.2),(0.4,1.8),(2,∞)Find the interval(s) of decrease.(−1.18,0.08),(3.18,4.92)Find the inflection points of the function.smallest x-value(x,y)=See image for details.largest x-value(x,y)=See image for details.Find the interval(s) where the function is concave up.(−∞,0.97),(2.80,∞)See image for details.Find the interval(s) where the function is concave down.

Asked Nov 20 at 03:54

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Basic Answer

Step 1: Find the Interval(s) of Increase

The intervals of increase for the function $f(x)=x^5-5x^4-x^3+28x^2-2x$ are given as:
$$(-\infty ,-0.2),(0.4,1.8),(2,\infty )$$

Step 2: Find the Interval(s) of Decrease

The intervals of decrease for the function are given as:
$$(-1.18,0.08),(3.18,4.92)$$

Step 3: Find the Inflection Points of the Function

The inflection points are:

• Smallest x-value: $(x,y)=\text{(See image for details)}$
• Largest x-value: $(x,y)=\text{(See image for details)}$

Step 4: Find the Interval(s) Where the Function is Concave Up

The intervals where the function is concave up are given as:
$$(-\infty ,0.97),(2.80,\infty )$$

Step 5: Find the Interval(s) Where the Function is Concave Down

The intervals where the function is concave down are given as:
$$(0.97,2.80)$$

Final Answer

• Intervals of increase: $(-\infty ,-0.2),(0.4,1.8),(2,\infty )$
• Intervals of decrease: $(-1.18,0.08),(3.18,4.92)$
• Inflection points: $(x,y)=\text{(See image for details)}$
• Intervals concave up: $(-\infty ,0.97),(2.80,\infty )$
• Intervals concave down: $(0.97,2.80)$