Derivatives and Antiderivative

Derivative means the same thing as

• slope of the tangent line

• slope of the normal line

• slope of the secant line

• the function’s value

Using this graph of f’(x), find the slope of the line tangent to f(x) at point c

• 0

• 1

• -1

• Not enough information

Find the slope at x = 3 of the equation f(x) = 3x²

• 6x

• 27

• 18

• 3x

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

Differentiate y= x³ + 2x

• 3x³+2x
• 3x²+2
• 3x+2
• 3x

What is the derivative of a constant, C?

• C
• 1
• 0

Find the derivative of the given equation
f(x) = x⁴ + 4x³ - 2x²

• x³ + x² - x
• 4x³ + 12x² + 4x
• 4x + 12x - 4x
• 4x³ + 12x² - 4x

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

• 1/2x
• -2x
• 2x
• -2x^-3

How many derivatives can you take of a function?

• only 3
• only 2
• only 1
• until you can no longer derive it

Find the derivative of the given equation
f(x) = x⁴ + 4x³ - 2x²

• x³ + x² - x
• 4x³ + 12x² + 4x
• 4x + 12x - 4x
• 4x³ + 12x² - 4x