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 mpg of the secant line PQ. iii. Let the point Q(x, f(x)) be the arbitrary point along the graph of f(x) where the value of x must be in between 1 and 2.5 (i.e. 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 mpg of the secant line PQ. iii. Let the point Q(x, f(x)) be the arbitrary point along the graph of f(x) where the value of x must be in between 1 and 2.5 (i.e. 1

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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