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Find the relative maxima, relative minima, horizontal points of inflection, and sketch the graph for y=1/6x^6-x^4+7

Question

Find the relative maxima, relative minima, horizontal points of inflection, and sketch the graph for 

y=1/6x^6-x^4+7

check_circleAnswer
Step 1

The given function is,

1
6
-x°
y=_r°- r*+7
4
6
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1 6 -x° y=_r°- r*+7 4 6

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Step 2

Relative minimum and relative maximum:

Obtain the critical points as follows.

Differentiating the function with respect to x,

d1
dx6
6
x* + 7
.6x - 4x3
=r-4x
Equate the above result to zero.
x-4x3 0
(x2-4)0
(x+2(x-2)0
x = 0 or x2 = 0 or x- 2 = 0
x 0 or x 2 or x = 2
Thus, the critical points are -2, 0, and 2
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d1 dx6 6 x* + 7 .6x - 4x3 =r-4x Equate the above result to zero. x-4x3 0 (x2-4)0 (x+2(x-2)0 x = 0 or x2 = 0 or x- 2 = 0 x 0 or x 2 or x = 2 Thus, the critical points are -2, 0, and 2

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Step 3

Find the values of y of the corresponding values...

1
5
6
At x 2 y(-2)° -(-2) +7 =;
3
1
At x 0, y(0) -(0)+7 = 7
6
1
5
6
At x 2, y(2) - (2)' +7 =
6
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1 5 6 At x 2 y(-2)° -(-2) +7 =; 3 1 At x 0, y(0) -(0)+7 = 7 6 1 5 6 At x 2, y(2) - (2)' +7 = 6

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Math

Calculus

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