Test 2 100 points Math 150 Name:

Always show work to defend your answer in a logical and organized fashion unless toldotherwise.

1. (10 points) Use the limit definition to compute the derivative function of f(x) = 2x2+ x.

2. (10 points) The position of a particle moving in a straight line is s(t) = et cos(t) centimeters after tseconds have elapsed. Find an expression for both the velocity and the acceleration at time t.

3. (10 points) Sketch the graph of the derivative for the function with graph shown below. Draw your

answer on the same axes.

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4. (10 points) Find

✓g � h� h

g

◆0

(2) if the values of h(x) and g(x) are given in the table below. Recall

(g � h)(x) = g(h(x)), a composition of functions.

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(2) g(1) g(2) g0(1) g0(2)2 1 2 4 2 3 �1 �3

5. (10 points) Find the equation of the tangent line to the curve y(x+ 2)� 2y =x2

y2� 2 at the point

(2, 1). Write your final answer in y = mx+ b form.

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6. Find derivatives for the following functions. Do not simplify. You do not need to show any work.

(a) (5 points) f(t) = t2esin(t)

(b) (10 points) h(x) =cos(4x2

)

ln(2 + x)

(c) (10 points) g(y) = arctan(y2)p

y + 2� 3y

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7. (10 points) Use implicit di↵erentiation to findd cos�1

(x)

dxwhere cos

�1(x) can also be written

arccos(x).

8. (15 points) A light on the ground shines on a wall 10 meters away. A meter tall child walks from the

light toward the wall at 1 meter per second. How fast is the child’s shadow on the wall changing

when they are 5 meters from the wall?

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