3.1 The DerivativeWed Oct 7

If f(x) = 2x^2 - 3, find the slope between the x values of 1 and

4

Test Review

Retakes this week

Recall, it is difficult to find the slope of a function at a particular point.

The Slope Problem

The Derivative at a point

• The derivative of a function f(x) at x = a is defined as:

• We can now find the equation of tangent lines at specific points

Ex 1• Find an equation of the tangent line to

the graph of f(x) = x^2 at x = 5

Ex 2Find the derivative of at x = 3

Ex 3Find the tangent line of f(x) = 1/x at x = 2

Closure

• Find the derivative f’(x) ofat x = 2 using the limit definition

• HW: p.126 #1, 3-6, 11-14, 27-43 odds, 51-55 odds

3-1 The DerivativeThurs Oct 8

Find the slope of the tangent line to y = f(x) at x = a

1) x^2 + 3, a = 12) 3x-2, a = 2

HW Review p. 126 #1 3-6 11-14 27-43 51-55

• 1) f’(3) = 30 29) y = -11t + 18• 3) f’(0) = 9 31) y = x• 4) f’(2) = 13 33) y = -1/64 x + 1/4• 5) f’(-1) = -2 35) y = -x - 1• 6) f’(2) = 12 37) • 11) f’(1,2) = 0, f’(4) = 1/2 f’(7) = 0 39) y = -1/16x + 3/4• 12) x > 7 41) • 13) f’(5.5) 43) f’(0) = 0; y = 1• 14) slopes of left/right diff 51) f(x) = x^3 and a = 5• 27) y = 22x - 18 53) f(x) = sin x and a = pi/6• 55) f(x) = 5^x and a = 2

The Derivative at a point• With a calculator:• MATH -> nDeriv• Function, x, x-value

• OR

• Graph -> 2nd -> Calc -> dy/dx -> type in x value

Derivative worksheet

ClosureJournal Entry: How do we use limits to find the slope of the tangent line to a curve?

HW: Finish worksheet if necessary