Question #aae8e

1 Answer
Steve M
Nov 15, 2016

See Below

Explanation:

Let f(x) = x^3 - e^-x f(x)=x3−e−x

Then f(0) = 0-e^0 = -1 f(0)=0−e0=−1
And, f(1) = 1 - e^-1 = 0.6321 f(1)=1−e−1=0.6321 (4dp)

Both e^-xe−x and x^3 x3 are continuous functions AA x in RR , and hence f(x) = x^3 - e^-x is a continuous function AA x in RR . As f(x) changes sign over the interval [0,1] then f(x)=0 must have a root in that interval, and consequently e^-x=x^3 has a solution in the interval.

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