3.1 The Derivative Tues Sept 22 If f(x) = 2x^2 - 3, find the slope between the x values of 1 and 4.

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Presentation transcript:

3.1 The Derivative Tues Sept 22 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

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

The derivative of a function The derivative of f(x) is the function f’(x): Lots of simplification will be involved!

Ex 1 Find the derivative of

Ex 2 Find the derivative of f(x) = 2x^2 - 5x + 7

Ex 3 Find the derivative of y = x^-2

Closure Journal Entry: How do we use limits to find the slope of the tangent line to a curve? HW: 3.1 p.126 #2, 5, 9, 11, 14, 33, 41, 47, p.139 #1 3 5