Differentiation (Calculus)

If a function has a first derivative that is negative, what does that tell you?

• The function is increasing

• The function is decreasing

• The concavity of the function is up

• The concavity of the function is down

If f'(x) = 0 what does that imply about the x value?

• It is a critical point, it is a possible max, min, or point of inflection.

• That the limit does not exist.

• cosx

• -cosx

• sec²x

• secxtanx

• sinx

• -sinx

• -cscx cotx

• -cot²x

Find the derivative of

• secx tanx
• sec²x
• cscx cotx
• -cscx cotx

Differentiate y= 12x^-2

• 24x^-1
• -24x^-3
• -24x^-1
• 6x^-3

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

Find the derivative of the given equation
f(x) = 1/x²

• 1/2x
• -2x
• 2x
• -2x^-3

Differentiate 6x^⅔.

• 4x^-⅓
• 4x^-⅔
• 6x^⅓
• 4x^⅓

Find the derivative of:
f(x) = (x - 4)(x + 7)

• 2x + 3
• 2x - 4
• 2x + 4
• 2x - 3