Determine whether the function has a maximum or minimum value. Then find the maximum or minimum value of the function. y = - x2 + 4x + 1

Select one:
a. min; 2
b. max;
c. min; -5
d. max; 5

Question

Determine whether the function has a maximum or minimum value. Then find the maximum or minimum value of the function.  y =  - x2 + 4x + 1

Select one:
a. min; 2
b. max;
c. min; -5
d. max; 5

hoblos · Answer

calculate the second derivative of the function (y'')
if it is positive --> it has a minimun
if it is negative--> it has a maximum

y' = -2x +4
y'' = -2  negative  , then we have maximum

to find it, we set y'=0 and solve for x

-2x+4 = 0   then x=2
y = -(2)^2 +4(2) +1 = 5
so it's d