3.1 The Derivative Wed 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 2 Find the derivative of at x = 3

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

Closure Find the derivative f’(x) of at x = 2 using the limit definition HW: p.126 #1, 3-6, 11-14, odds, odds

3-1 The Derivative Thurs Oct 8 Find the slope of the tangent line to y = f(x) at x = a 1)x^2 + 3, a = 1 2)3x-2, a = 2

HW Review p. 126 # ) f’(3) = 3029) y = -11t ) f’(0) = 931) y = x 4) f’(2) = 1333) y = -1/64 x + 1/4 5) f’(-1) = -235) y = -x - 1 6) f’(2) = 1237) 11) f’(1,2) = 0, f’(4) = 1/2 f’(7) = 0 39) y = -1/16x + 3/4 12) x > 741) 13) f’(5.5)43) f’(0) = 0; y = 1 14) slopes of left/right diff51) f(x) = x^3 and a = 5 27) y = 22x ) 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 -> 2 nd -> Calc -> dy/dx -> type in x value

Derivative worksheet

Closure Journal Entry: How do we use limits to find the slope of the tangent line to a curve? HW: Finish worksheet if necessary