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MA 160 Using Rules of Differentiation Section 1.
- Differentiate each of the following functions. Be sure to get the function into an appropriate form for applying rules of differentiation before finding a derivative. Write answers with no negative exponents.
(a) f ( ) x = 2 x^4 โ 6 x^3 + 8 x โ 9 (b)
2 2
x g x x
(c)
y 6 x x
= + (d)^ h x ( ) = ( x^2 + 7)( x^3 โ3)
- Let 3 2
y = x โ x + x +.
(a) Write the equation of the tangent line to this function when x = 3 on the curve.
(b) At what value or values of x does this function have a horizontal tangent line?
OVER
- Use the general power rule to differentiate each of the following functions. Write answers with no negative exponents.
(a) f ( ) x = ( x^3 + 4)^6 (b) y = x^2 + 9
(c)
g x x
(d) 3 4
y x x
- U.S. sales of gift cards have been increasing in recent years. Sales of these cards in
billions of dollars are projected to be S t ( ) = โ0.6204 t^3 + 4.671 t^2 + 3.35 t + 47.4, where 0 โค t โค 5 , and t = 0 corresponds to 2003.
(a) Find S^ (5)and write a sentence interpreting your answer in the context of this situation.
(b) Find S โฒ(5) and write a sentence interpreting your answer in the context of this situation.
