Question

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

Answer 1

9

Explanation:

Answer 2

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

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`