Question

Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.)

f (x) = x2 + 9x − 4 relative minimum
(x, y) =
relative maximum (x, y) =

please help me
...?

Answer 1

Find all relative extrema.


`f (x) = x^2 + 9x -4 \\f'(x)=(x^2 + 9x -4)'=2x+9 \\f'(x)=0 \\2x+9=0 \\2x=-9 \\x=- (9)/(2)`

Determine if relative extrema is minimum or maximum.


`f''(x)=(2x+9)'=2\ \textgreater \ 0 \Rightarrow x_(min)=- (9)/(2)`

`y_(min)=(- (9)/(2) )^2+9(- (9)/(2))-4= (81)/(4)- (81)/(2) -4=(81)/(4)- (162)/(4) - (16)/(4) =- (97)/(16) \\ \\(x,y)=(- (9)/(2),- (97)/(16) )`