3.2 The Power Rule Thurs Oct 22 Do Now Find the derivative of:

Quiz Review Retakes by Tues

Computations of Derivatives Thm- For any constant c, Note, when y = c, the slope of that line is always horizontal. Therefore, its derivative must equal 0

Thm- Let f(x) = x, then Proof: Note: This means that the derivative of any linear function is equal to the coefficient

Power Rule Let’s take a look at the different powers of x. Can you see the pattern in the table? F(x)F’(x) 10 X^11 X^22x X^33x^2 X^44x^3

Power Rule cont’d Power Rule - For any real number n, Note: The power rule works for negative exponents, as well as fraction exponents.

Ex 3.1 Find the derivatives of

Ex 3.2 Find the derivatives of

General Derivative Rules Thm- If f(x) and g(x) are differentiable at x and c is any constant, then 1) 2) 3)

General Deriv. Rules Remember, to rewrite any expressions so they have exponents! And split the expression into separate terms! You try: Find the derivative of each: 1) 2) 3)

Closure Hand in: Find the derivative of: 1) 2) HW: p.139 #7-13 odds, 21-27odds, 33, 49

3.2 Power Rule cont’d Fri Oct 23 Do Now: Find the derivative of: 1) 2)

HW Review p.139 # , 33, 49 7)-3233) 32s ) 1/349) a) 11) b) 13) c) 21) 23) 25) 27)

Derivative of e^x The derivative of f(x) = e^x is

Finding tangent line equations Now that we have the power rule, it is much easier to find the equations of tangent lines. EX: Find the tangent line to the graph at x = 2

Differentiability and Continuity If f is differentiable at x = c (the derivative is defined at c) then f is also continuous at c

Derivative Info The derivative can tell us when a function is increasing (+), decreasing (-), or horizontal (0) This makes finding the vertex of a function easier

Closure Journal Entry: How does the power rule work? What does a derivative tell us about a function? HW: p. 139 #15-19 all,

3.2 Power Rule Practice Fri Oct 26 Do Now Find the derivative of the following: 1) 2)

HW Review: 139 #15-19, ) y = 32x ) A = f(x) 16) y = -2/125 x + 3/25B = h(x) 17) y = -3x - 32C = g(x) 18) y = 1/12 x + 4/3 19)a) 12e^xb) 25-8e^tc) e^(t-3) 29) 0 31) 43) A - 3, B - 1, C - 2, D - 3

Derivative Rules so far: Power Rule E^x Constant Rule Breaking up functions into individual terms

Practice Green book worksheet p.184 #5-23

Closure Journal Entry: How does the graph of a function relate to the graph of its derivative? HW: Finish worksheet p.184 #5-23

HW Review p odds 5)3x^2 -221) 7)6x23) 9) 0 11) 13) 15) -5x^(-3/2) -2 17) 19)

HW Review p evens 6) 8) 10) -4 12) 14) 16) 18) 20) 22)