derivative

the first derivative of f(x) = 3x²

• f'(x)=3x

• f'(x)=3x²

• f'(x)=6x

• f'(x)=6x²

the second derivative of f(x) = 3x² + 5x

• f''(x) = 6x

• f''(x) = 3x + 5

• f''(x) = 6x + 5

• f''(x) = 6

find x such that f'(x)=0 for f(x) = 3x² - 5x

• x = 0

• x = 1/6

• x = 5/6

• x = 6/5

the value of the first derivative of a function tells you the

• slope of the tangent line

• the equation of the tangent line

• the maximum of the function

• where the function is undefined

the slope of the tangent line at a function's local max will be

• undefined

• positve

• negative

• 0

you might find a local min of a function where you find that the tangent line is

• vertical

• horizontal

• parallel to the function

• undefined

for a position function the first derivative can tell you

• the velocity function

• the position function

• the acceleration function

• the initial position

for a position function the second derivative can tell you the

• initial position

• the velocity function

• the acceleration function

• the final position

the second derivative of f(x) = 3x²

• f''(x)=3x

• f''(x)=3x²

• f''(x)=6

• f''(x)=6x

the first derivative of f(x) = 3x² + 5x

• f'(x) = 6x

• f'(x) = 3x + 5

• f'(x) = 6x + 5

• f'(x) = 6