PRE- TEST - Fun with Differentiation

What is an algebraic function?

• A function that only includes trigonometric terms.

• A function that is defined by a logarithmic equation.

• A function that has no variables or constants.

• An algebraic function is a function defined by a polynomial equation.

Which of the following is an algebraic function?

• A polynomial function, such as f(x) = x^2 + 3x + 2.

• A logarithmic function, such as f(x) = log(x).

• An exponential function, such as f(x) = 2^x.

• A trigonometric function, such as f(x) = sin(x).

What is the derivative of x^2?

• x

• 2x^2

• 2x

• x^3

What is the power rule in differentiation?

• The power rule states that f'(x) = n*x^n for f(x) = x^n.

• The power rule applies only to polynomial functions with even exponents.

• The power rule in differentiation is f'(x) = n*x^(n-1) for f(x) = x^n.

• The power rule is used to find the integral of a function.

If f(x) = x^3, what is f'(x)?

• 2x^2

• 3x^2

• x^2 + 3

• 3x^3

Which function is not algebraic?

• e^x

• x^2 + 3

• log(x)

• sin(x)

What is the derivative of 5x?

• x

• 5x^2

• 10

• 5

What does differentiation help us find?

• The rate of change of a function or the slope of the tangent line.

• The roots of a polynomial.

• The area under a curve.

• The maximum value of a function.

If f(x) = x^4, what is f'(x)?

• 3*x^2

• x^3

• 4*x^3

• 2*x^4

What is the derivative of a constant?

• Undefined

• The constant itself

• 0

• 1