Final Exam Review (Units 1-5)

Front

Find the derivative of the function: y = 3ln(x^2 - 3)

Back

Front

Will a linear approximation to the graph of f(x) = -x^2 + 3x overestimate the actual function values of f?

Back

Yes, it will overestimate actual function values because due to the concavity of f, any tangent drawn will be above the curve.

Front

Back

Front

Find f'(4) for the function f(x).

Back

The value is -4.

Front

Differentiate the function f(x) = x^3 + 3cot(x).

Back

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.

Front

Explain the concept of linear approximation.

Back

Linear approximation uses the tangent line at a point to estimate the value of a function near that point.

Front

What is concavity in relation to functions?

Back

Concavity describes the direction of the curvature of a function; a function is concave up if its second derivative is positive and concave down if its second derivative is negative.

Front

State the product rule for differentiation.

Back

Front

What is the chain rule in differentiation?

Back