consider-the-function-fx2x24x1fleftxright-2x24x1-and-nbspon-the-interval-12leftl

Question

Consider the function $f (x) = - 2 x^{2} + 4 x + 1$ on the interval $open bracket negative 1 comma 2 close bracket$ . Find the critical points of $f$ and use the First Derivative Test to classify these points. Then, determine the absolute maximum and minimum values of $f$ on the specified interval (if there are any).

Accepted Answer

Critical point: $x=1$

Local maximum at $x=1$

Absolute maximum: $3$ at $x=1$

Absolute minimum: $-5$ at $x=-1$

Answer

Critical point: $x=1$

Local maximum at $x=1$

Absolute maximum: $3$ at $x=1$

Absolute minimum: $negative 6$ at $x=-1$

Answer

Critical point: $f (x) = - 2 x^{2} + 4 x + 1$

Local minimum at $x = - 1$

Absolute maximum: $4$ at $x=1$

Absolute minimum: $-5$ at $x equals 2$

Answer

Critical point: $x=1$

Local minimum at $x=-1$

No absolute extrema