Concept explainers
In Example 6 in this section, we were given
(a) the instantaneous rate of change of f(x) at x = 6.
(b) the slope of the tangent to the graph of y = f(x) at x = 6.
(c) the point on the graph of y = f(x) at x = 6.
EXAMPLE 6 Tangent Line
Given
(a) the derivative of f(x) at any point (x, f(x)).
(b) the slope of the tangent to the curve at (1, 16).
(c) the equation of the line tangent to
Solution
(a) The derivative of f(x) at any value x is denoted by f'(x) and is
(b) The derivative is
(c) The equation of the tangent line uses the given point (1, 16) and the slope m = 8. Using
The discussion in this section indicates that the derivative of a function has several interpretations.
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Mathematical Applications for the Management Life and Social Sciences
- YOUR TURN Find an equation of the curve whose tangent line has slope f(x)=3x1/2+4 and passes through the point (1,2).arrow_forwardAt what point on the graph of fx=-5x2+4x-2 is the slope of the tangent line 6?arrow_forwardIf the instantaneous rate of change of f(x) with respect to x is positive when x=1, is f increasing or decreasing there ?arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill