Derivatives - Product & Quotient Rules

Which of the following is not a correct notation for derivative?

• f'(x)

• y'

• dy

• dy/dx

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• slope of the secant line

The three situations where derivatives fail to exist are at corners or cusps, at a vertical tangent, and...

• at a horizontal tangent

• at a discontinuity

• at points of inflection

• at intercepts

How do you find horizontal tangent lines?

• Find where the derivative is undefined

• Find where the derivative equals zero

• Find where the derivative equals one

• Find where the derivative is negative

What is the derivative of ax?

• a
• x
• 1
• 0

What is the derivative of a constant, C?

• C

• 1

• 0

• DNE

What is the derivative of xⁿ?

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

At which point(s) on the graph are the slopes of the tangent line to the graph equal to zero?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

At which point(s) on the graph are the slopes of the tangent line to the graph negative?

• at C only

• at points A, C and E only

• at point B and D only

• at point D only

Differentiate y = x³ + 2x

• 3x² + 2x

• 3x² + 2

• 3x + 2

• 3x