SOLUTION: For each of the following expressions, calculate the value of x which gives y a stationary value. Determining whether this value of y is a minimum or a maximum. Give your answers

Question 1194169: For each of the following expressions, calculate the value of x which gives y a stationary value.
Determining whether this value of y is a minimum or a maximum. Give your answers correct to 3 significant figures where necessary.
a) y = x^2 + (2x-1)^2
b) y = 2πx - (x-2)^2
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
y=x^2+(2x-1)^2
y'=2x+2(2x-1)*2=2x+8x-4=10x-4
set that equal to 0
10x=4
x=0.4
2nd derivative is 10 and is always positive so this is a minimum
alternative way into expand function to x^2+4x^2-4x+1=5x^2-4x-1
find vertex by x=-b/2a=-4/-10 or +0.4

--
y'=2 pi-2(x-2)=2pi-2x+4
set equal to 0
2x=2pi+4
x=2+pi or 5.28
y''=-2, and this will be a maximum.

RELATED QUESTIONS
Determine the value of x , where 0 ≤ x ≤ π , for which the curve y = 2cosx + 3sinx... (answered by greenestamps)

In determining the p-value for reporting the study's findings, which of the following is... (answered by stanbon)

Given that y=-2/3x^3+5/2x^2-2/x,find the two values of x for which y is stationary. Show... (answered by Alan3354)

Brianna’s teacher asks her which of these three expressions are equivalent to each... (answered by josgarithmetic)

Which of the following expressions has a positive value for all x > 0 and y < 0? A)... (answered by josgarithmetic)

Decide whether the following equation defines y as a function of x. y=17sqrt x a)... (answered by fractalier)

Which of the following is not a question to ask when determining whether an expression... (answered by Fombitz)

Complete the equation of the line L satisfying each of the following sets of geometric... (answered by Fombitz)

If y=13, which one of the following expressions will produce a value of 4? y+14... (answered by Alan3354)