AP Calculus AB 2.2 Defining the Derivative and Derivative Notation Question Bank

Practise AP Calculus AB 2.2 questions by using derivative notation to find slopes and tangent lines in varied contexts.

Exam points

find tangent slopes and equations using derivative rules, tables, implicit or parametric data
solve tangent-line conditions such as parallel slopes, intercepts and path directions

5. Let f be the function whose graph is shown above; the graph of f consists of

three line segments.

Let g be a differentiable function. The table above gives values of g and its

derivative $g^{\prime}$ at various values of x.

(a) Let w be the function defined as w(x)=f(3 x)+g(x). Find an equation

of the tangent line to w at x=1.

AB 5. (a) For the tangent line, we need a point and a slope. Point: w(1)=

f(3)+g(1)=2+2=4. Slope: $w^{\prime}(x)=3 f^{\prime}(3 x)+g^{\prime}(x) \Rightarrow w^{\prime}(1)=$

$3 \cdot f^{\prime}(3)+g^{\prime}(1)=3(2)+5=11$

All question bank results loaded