Calculus Derivatives Quiz

The derivative of a function at a point represents:

• The slope of the secant line at that point.

• The slope of the tangent line at that point.

• The area under the curve up to that point.

• The y-intercept of the function.

The derivative of f(x) at point 'a', denoted f'(a), is defined as:

• lim (h→0) [f(a) - f(a+h)]/h

• lim (h→0) [f(a+h) - f(a)]/h

• f(a+h) - f(a)

• f(a) - f(a+h)

If a function is differentiable at a point, it is also:

• Continuous at that point

• Discontinuous at that point

• Undefined at that point

• Has a vertical asymptote at that point

A function can fail to be differentiable at a point if:

• It is continuous at that point.

• It has a sharp corner or cusp.

• The limit exists at that point.

• It has a smooth curve at that point.

The second derivative of a function represents:

• The slope of the tangent line.

• The rate of change of the first derivative.

• The area under the curve.

• The y-intercept.

What is the derivative of f(x) = 5x³ - 2x + 7?

• 15x² - 2

• 15x² + 2

• 5x² - 2x + 7

• 15x - 2

What is the derivative of f(x) = sin(x)?

• cos(x)

• -cos(x)

• -sin(x)

• sin(x)

What is the derivative of f(x) = eˣ?

• eˣ

• 1

• 0

• x*eˣ⁻¹

What is the derivative of f(x) = ln(x)?

• 1/x

• x

• eˣ

• 1

The Chain Rule is used to differentiate:

• Sums of functions

• Products of functions

• Composite functions

• Quotients of functions