Howard J. answered • 10/22/19

Principal Mechanical Engineer with >30 years' math coaching experience

#### f(x)=6x^2−10x+10,0≤x≤9

What is the absolute maximum and minimum of this function on the given interval.

y=6x^{2}-10x+10 is a concave up parabola.

dy/dx=12x-10=0

d^{2}y/dx^{2}=12 > 0 so that extrema is a minimum.

and x=10/12=5/6 at the vertex

when x=5/6, y=6(5/6)^{2}-10(5/6)+10=25/6-50/6+10=-25/6+60/6=35/6≅5.83

so the vertex (minimum) is at (5/6,35/6)

The interval is [0,9]

When x=0, y=10

When x=9, y=6(9)^{2}-10(9)+10=6(81)-90+10=406

**Absolute maximum is 406**

**Absolute minimum is 35/6≅5.83**