Unit 2: Derivatives Part I · 03/02/2018 · Derivative of the function f at the point x = a is...
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1 Unit 2: Derivatives Part I 3.1 Derivatives of a function Pages 99 - 108 Complete the derivative investigation 1. Using the graph, estimate the slope of the tangent line at the following values of x. Plot your results on the same axis: a) x = ‐2 b) x = ‐1 c) x = 0 d) x = 1 e) x = 2
Transcript of Unit 2: Derivatives Part I · 03/02/2018 · Derivative of the function f at the point x = a is...
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Unit 2: Derivatives Part I
3.1 Derivatives of a function Pages 99 - 108
Complete the derivative investigation1. Using the graph, estimate the slope of the tangent line at the following values of x. Plot your results on the same axis:a) x = ‐2 b) x = ‐1 c) x = 0
d) x = 1 e) x = 2
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2. Using the graph, estimate the slope of the tangent line at the following values of x. Plot your results on the same axis:a) x = ‐2 b) x = ‐1 c) x = 0
d) x = 1 e) x = 2
Domain of f' the set of points in the domain of f for which the limit exists; may be smaller than the domain of f.
If the derivative exists, then it is said that f is differentiable at x.
Differentiable function A function that is differentiable at every point of its domain.
Derivative of a function is the function that is used to calculate the slope of the tangent line for a given function.
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EXAMPLE 1 Applying the Definition Page 99
Differentiate
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More examples:Use the definition of derivative to differentiate the following:
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You Try:Use the definition of derivative to differentiate the following:
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Derivative of the function f at the point x = a is given by:
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The previous exercises determined the function or formula for the derivative. The derivative can also be determined at an indicated value of a using the following formula:
EXAMPLE 2 Applying the Alternate Definition Page 100
Differentiate at x = 9 using the alternate definition.
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More examples:Use the alternate definition of derivative to differentiate the following:
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To Summarize:
To Find: Use the formula:
The slope(derivative) of a curve at a certain point
The derivative at any point x(Definition of Derivative)* Gives the formula that can be used to find the slope of any tangent line to the curve
The derivative using the alternate formula given a point
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Additional Example:Sketch the function described by the following: f(0) = 0 f(x) is continuous for all values of x
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#21 page 106
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#23 page 106
#25 (i)
(ii)
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(iii)
(iv)
(v)
