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KengaRu [80]
3 years ago
10

Based on the extreme value theorem, what is the maximum value of f(x) = –x2 + 6x over the interval [1, 4]?

Mathematics
2 answers:
marysya [2.9K]3 years ago
6 0

Answer:

9

Step-by-step explanation:

Tju [1.3M]3 years ago
3 0

Answer:

Maximum\ value\ =9 ,at\ x=3

Step-by-step explanation:

From the question we are told that:

Function given

f(x) = -x^2 + 6x

Co-ordinates

(x,y)=[1, 4]

Generally the second differentiation of function is mathematically given by

-2x+6

Therefore critical point

x=3

Generally the substitutions of co-ordinate into function is mathematically given by

For 1

F(1)=-(1)^2 + 6(1)\\F(1)=5

For 4

F(4)=-(4)^2 + 6(4)\\F(4)=8

For critical point 3

F(3)=-(3)^2 + 6(3)\\F(3)=9

Therefore the maximum value of f(x) = –x2 + 6x over the interval [1, 4] is given by

Maximum\ value\ =9 ,at\ x=3

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