identify the vertex of the graph. Tell whether it is a minimum or maximum. a) (0,0); maximum b) (0,1); maximum c) (0,1); minimum D) ( 0,0); minimum​

a) The function has a maximum at  x = 29,59

b) 99,32 %

Step-by-step explanation:

f(x) = -0,11*x² + 6,51*x + 3

Then:

f´(x) = -0,22*x + 6,51

If   f´(x) = 0   then    - 0,22*x + 6,51 = 0

0,22*x = 6,51

x = 6,51/0,22    ⇒     x = 29,59

if we get the second derivative

f´´(x) = - 0,22       f´´(x) < 0   then we have a maximun at x = 29,59

a) the function has a maximum

b) 29,59 years after 2000   ( in 2030 )

c) f(x) = - 0,11*x² + 6,51*x + 3

f(29,59) = - (0,11)* (29,59)² + 6,51*29,59 + 3

f(29,59) = 99,32 %