(Solved): HW Supplement: Equation of Tangent Line Namt Let f(x)=0.1x^(3)-2.5x+3.4 a). Use a graphing tool to ...
HW Supplement: Equation of Tangent Line Namt Let
f(x)=0.1x^(3)-2.5x+3.4a). Use a graphing tool to graph of
f(x)for the window
x[-6,6]and
y[-5,10]and find
f(0),f(6), and
f(4). Then plot and label the three points and reproduce a sketch of the graph below. b. Use a ruler to sketch, above, the secant line between the points where
x=0and
x=6. The slope of this secant line is the AVERAGE rate of change of
f(x)over the interval
0,6. c. Find the average rate of change of
f(x)over the interval
0,6. (show work). d. Use a ruler to sketch, above, the tangent line to
f(x)at the point where
x=4. e. Is the slope of the tangent line greater or less than the slope of the secant line drawn? (guess) f. Use the basic rules to find
f^(')(x).
f(x)=0.1x^(3)-2.5x+3.4,f^(')(x)=The instantaneous rate of change of
fat
x=4is the slope of the tangent line at that point. The slope of the tangent to a function at a point is the derivative at that point. g. Find
f^(')(4)=and compare this slope to the slope of the secant from (c). h. Use your results in part
gto find the equation of the tangent line to
f(x)at
x=4. Pt:
(4,f(4))Slope:
m=f^(')(4)Equation of line:
y-y_(o)=m(x-x_(o))