3. 22/28 points 1 Previous Answers SCalcCC443 026 Consider the function below. (
ID: 2877578 • Letter: 3
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3. 22/28 points 1 Previous Answers SCalcCC443 026 Consider the function below. (Give your answers correct to three decimal places. If you need to use -co or an, enter-INFINITY or INFINITY) h(x) 4x5 7x3x (a) Find the intervals of increase.(Enter the intervals that contain smaler numbers first) 1.000 U(1000 INFINITY1 Find the intervals of decrease. (Enter the interval thot contains smaller numbers first.) 1 000 0224 1,000) (b) Find the local minimum values. h(x) 0 112 h(x)-4000 (smaller x value) (larger x value) × h(x)- 4 000 Find the local maximum values. h(x)-4000 (x)-0112x (larger x value) (smaller x value) (c) Find the inflection points 0724 C0.000 (0724 2380 x(smallest x value) 0.000 2 380 X ) (largest x value) Find the intervals the function is concave up. (Enter the interval that contains smaller numbers first.) Find the intervals the function is concave down. (Enter the interval that contains smaller numbers first.) INFINITY0724 UC00000724 (d) Use this information to sketch the graph of the function. (Do this on paper. Your instructor imay ask you to turn in this graph, ) Talk to a Tuter Need Help?Read Submit Answer Save Progress Practice Another VersionExplanation / Answer
(a) f(x) = 4x^5 - 7x^3 + x
f'(x) = 20x^4 - 21x^2 + 1
20x^4 - 21x^2 + 1 = 0
20x^4 - 20x^2 - x^2 + 1 = 0
20x^2 (x^2 - 1) - 1(x^2 - 1) = 0
(20x^2 - 1)(x^2 - 1) = 0
x = -1/20. 1/20, -1, 1 = -0.2236, 0.2236, -1, 1
f"(x) = 80x^3 - 42x
f"(-1/20) = 8.5
f"(1/20) = -8.5
f"(-1) = -38
f"(1) = 38
So, f(x) has local minimums at x = -1/20 and x = 1
f(-1/20) = -0.148
f(1) = -2
Local minimums are (-0.224, -0.148) and (1, -2)
So, f(x) has local maximums at x = 1/20 and x = -1
f(1/20) = 0.148
f(-1) = 2
Local maximums are (0.224, 0.148) and (-1, 2)
(b) f"(x) =80x^3 - 42x = 0 gives x = 0, -3.320, 3.320
f(0) = 0
f(-3.320) = 0.725
f(3.320) = -0.725
The inflection points are (0, 0), (-3.320, 0.725, 3.320, -0.725)
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