The function​ f(x) is continuous on

left parenthesis negative infinity comma infinity right parenthesis(−∞,∞).

Use the given information to sketch the graph of f.

​ f(negative 6−6​)equals=00​,

​f(00​)equals=negative 12−12​,

​f(66​)equals=00​;

f prime left parenthesis 0 right parenthesis equals 0f′(0)=0​,

f prime left parenthesis negative 6 right parenthesisf′(−6)

and

f prime left parenthesis 6 right parenthesisf′(6)

are not​ defined;

f prime left parenthesis x right parenthesisf′(x)greater than>0

on

left parenthesis 0 comma 6 right parenthesis(0,6)

and

left parenthesis 6 comma infinity right parenthesis(6,∞)​;

f prime left parenthesis x right parenthesisf′(x)less than<0

on

left parenthesis negative infinity comma negative 6 right parenthesis(−∞,−6)

and

left parenthesis negative 6 comma 0 right parenthesis(−6,0)​;

f double prime left parenthesis negative 6 right parenthesisf′′(−6)

and

f double prime left parenthesis 6 right parenthesisf′′(6)

are not​ defined;

f double prime left parenthesis x right parenthesisf′′(x)greater than>0

on

left parenthesis negative 6 comma 6 right parenthesis(−6,6)​;

f double prime left parenthesis x right parenthesisf′′(x)less than<0

on

left parenthesis negative infinity comma negative 6 right parenthesis(−∞,−6)

and left parenthesis 6 comma infinity right parenthesis(6,∞)

Question content area bottom

Part 1

Choose the correct graph of f below

A.

-1414-1414xy

A coordinate system has a horizontal x-axis labeled from negative 14 to 14 in increments of 2 and a vertical y-axis labeled from negative 14 to 14 in increments of 2. From left to right, a curve falls at an increasing rate to (negative 6, 0), rises at a decreasing rate to a maximum at (0, 12), falls at an increasing rate to (6, 0), and then rises at a decreasing rate.

B.

-1414-1414xy

A coordinate system has a horizontal x-axis labeled from negative 14 to 14 in increments of 2 and a vertical y-axis labeled from negative 14 to 14 in increments of 2. From left to right, a curve rises at a constant rate to (negative 6, 0), falls at a decreasing rate to a minimum at (0, negative 12), rises at an increasing rate to (6, 0), and then falls at a constant rate.

C.

-1414-1414xy

A coordinate system has a horizontal x-axis labeled from negative 14 to 14 in increments of 2 and a vertical y-axis labeled from negative 14 to 14 in increments of 2. From left to right, a curve falls at an increasing rate to (negative 6, 0), falls at a decreasing rate to a minimum at (0, negative 12), rises at an increasing rate to (6, 0), and then rises at a decreasing rate.

D.

-1414-1414xy