AP Calculus AB 2.6 Derivative Rules Question Bank

Practise AP Calculus AB 2.6 questions using linearity: constants, sums, differences and constant multiples.

Exam points

differentiate sums and differences term by term
factor constants through derivatives and evaluate the result

[Maximum number: 1]

Let be the function defined by $f(x)=b x^{2}+3 b x+b^{2}+\frac{1}{x^{2}}$ , where b is a nonzero constant. Which of the following is an expression for $f^{\prime}(x)$ , the derivative of f(x) ?

$2 b x+3 b-\frac{2}{x}$

$2 b x+3 b-\frac{2}{x^{3}}$

$2 b x+3 b+b^{2}-\frac{2}{x^{3}}$

$x^{2}+3 x+2 b$

g(x)=\left\{\begin{array}{lll} x^{2}+1 & \text { for } & x<3 \\ 13-x & \text { for } & x \geq 3 \end{array}\right.

All question bank results loaded

FUN-3.A—Calculate derivatives of familiar functions—Topic 2.6 question 1