Answer to Question #258910 in Calculus for Pankaj

Question #258910

Is the function f :[3, 4] ➡R defined by f(x) = x^2 -x is a monotonic in its domain

1
Expert's answer
2021-11-01T17:50:46-0400
f(x)=x2x,x[3,4]f(x)=x^2-x, x\in[3, 4]

f(x)=(x2x)=2x1f'(x)=(x^2-x)'=2x-1

If x[3,4],x\in[3, 4], then f(x)>0f'(x)>0 and f(x)f(x) is (strictly) increasing on [3,4].[3, 4].

Therefore the function f(x)=x2x,x[3,4]f(x)=x^2-x, x\in [3,4] is a monotonic in its domain.


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