1. Using the table of values, estimate the slope of a tangent line tangent to the curve f(x) = x³ – 27 at x = 4. What is the equation of a tangent line at point P(4,f (4)? i. Sketch the graph of f(x) and make a tangent line at point P. Label the graph and the tangent line. ii. Consider point Q(2.5, f(2.5)) along with the graph of f(x). Make a line connecting point P and point Q. Label the line by "Secant Line PQ". Find the slope mpq of the secant line PQ.
1. Using the table of values, estimate the slope of a tangent line tangent to the curve f(x) = x³ – 27 at x = 4. What is the equation of a tangent line at point P(4,f (4)? i. Sketch the graph of f(x) and make a tangent line at point P. Label the graph and the tangent line. ii. Consider point Q(2.5, f(2.5)) along with the graph of f(x). Make a line connecting point P and point Q. Label the line by "Secant Line PQ". Find the slope mpq of the secant line PQ.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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