AP Calculus AB 2.2 Defining the Derivative of a Function and Using Derivative Notation Questions

Practise AP Calculus AB 2.2 questions by connecting derivative limits with tangent slopes and equations across representations.

Exam points

connect difference-quotient limits with derivative notation and instantaneous slope
write tangent-line equations from derivatives, tables, graphs and parametric motion

[Maximum number: 1]

$\lim _{h \rightarrow 0} \frac{e^{2+h}-e^{2}}{h}$ is

$e^{2}$

$2 e^{2}$

nonexistent

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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