Use the Intermediate Value Theorem to show that there is

Khaleesi Herbert

Khaleesi Herbert

Answered question

2021-09-15

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. x4+x3=0, (1,2)

Answer & Explanation

SchepperJ

SchepperJ

Skilled2021-09-16Added 96 answers

Step 1
Let f(x)=x4+x3 for all x1, 2. We are looking for a number c[1, 2] such that f(c)=0. Function f is continuous on the closed interval [1, 2] so we can use Intermediate Value Theorem. We take a=1, b=2, N=0 in intermediate Value Theorem. We have:
f(1)=14+13=1<0
f(2)=22+23=15>0
Thus f(1)<0<f(2), that is , N=0 is a number between f(1) and f(2) so the mentioned theorem says there is a number c between 1 and 2 such that f(c)=0. We conclude that initial equation has at least one root c[1, 2]
f(1)=14+13=1<0
f(2)=24+23=15>0
so there exist c1, 2 such that f(x)=0

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