Answer:
[tex]Maximum\ value\ =9 ,at\ x=3[/tex]
Step-by-step explanation:
From the question we are told that:
Function given
[tex]f(x) = -x^2 + 6x[/tex]
Co-ordinates
(x,y)=[1, 4]
Generally the second differentiation of function is mathematically given by
[tex]-2x+6[/tex]
Therefore critical point
[tex]x=3[/tex]
Generally the substitutions of co-ordinate into function is mathematically given by
For 1
[tex]F(1)=-(1)^2 + 6(1)\\F(1)=5[/tex]
For 4
[tex]F(4)=-(4)^2 + 6(4)\\F(4)=8[/tex]
For critical point 3
[tex]F(3)=-(3)^2 + 6(3)\\F(3)=9[/tex]
Therefore the maximum value of f(x) = –x2 + 6x over the interval [1, 4] is given by
[tex]Maximum\ value\ =9 ,at\ x=3[/tex]
