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10. (6pts.) Show that the derivative of f(x) = 1 + 8x^ 2 is f ‘(x)...

10. (6pts.) Show that the derivative of f(x) = 1 + 8x^ 2 is f ‘(x) = 16x by using the definition of the derivative as the limit of a difference quotient.

11. (5pts.) If the area A = s^ 2 of an expanding square is increasing at the constant rate of 4 square inches per second, how fast is the length s of the sides increasing when the area is 16 square inches?

12. (5pts.) Find the intervals where the graph of y = x ^3 − 5x^ 2 + 2x + 4 is concave up and concave down, and find all the inflection points.

14. (6pts.) Find the absolute maximum and minimum values of f(x) = x ^3 −3x on the closed interval [0, 3].

15. (6pts.) A particle moves along the x-axis with an acceleration given by a(t) = 6t + 2, where t is measured in seconds and s (position) is measured in meters. If the initial position is given by s(0) = 3 and the initial velocity is given by v(0) = 1 then find the position of the particle at t seconds.


18. (5pts.) Find the area under the curve y = 2 + 2e^ x from x = 0 to x = 1



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