Use the Intermediate Value Theorem to show that there is a root of the given equ

Question

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.

-1 points scacct8 25053 nwa Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval, rx) X1 x 8 is -select on the closed Int CI, 2], f(1) and fi2) Since -6 v 10, there is a number c In (1, 2) such that f(c) by the Intermediate Value Th Thus, there is a Selett Uf e euuation x4 X 0 in the interval (1, 2 -1 points scacct8 2.5.055 nwa use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex 6 5x, 0, 1 The equation cr 6 5x is equivalent to the equation (x) c 6 5x 0, fx s continuous on the interval ro, 11, f(0) and (1) Since Select. Select there is a number c in (0 1) such that fc) 0 by the Intermediate value Theorem. hus, there is a root of the equation ex 6 Sx, In the Interval (0, 1). My Notes My Notes

Explanation / Answer

f(x) is continuous on the interval (1,2) ,f(1)=-6 and f(2)=10,since -6<0<10,there is a number c in(1,2) such that f(c)=0 by the intermediate value theorem .Thus there is a root of the equation x^4 +x-8 in the interval (1,2)

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