AP Calculus AB Cha 2 C Determine the Equation of a Line Tangent to a Curve At a Given Point Questions

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.

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

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

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