find the absolute maximum and minimum values of the function f(x) = x^3 - 3x , x= [0,2]
Answers
Answer:
find the absolute maximum and minimum values of the function f(x) = x^3 - 3x , x= [0,2]
Step-by-step explanation:
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Answer:
Step-by-step explanation:To get absolute maximum we follow below steps:
1) Get all critical points i.e we take derivative and find roots by equating it to zero.
2) Evaluate function at all critical points(if falling in given range) & at end points specified in question
3) The largest value in above step will be absolute maximum
Step1
f(x)=x
3
−3x+2;0⩽x⩽2
f
′
(x)=3x
2
−3=0⇒x=±1
Our critical points are +1 & -1, but as given in question we have to find absolute maximum in range [0,2] only. Hence we will reject -1
Step2
Evaluating f(x) at critical points & at end points:
f(1)=1−3+2=0
f(0)=0−0+2=2
f(2)=8−6+2=4
Step3
From above we can see f(x) achieves maximum value of 4 at x=2 in range xϵ[0,2]