# System Week 6 Secant Lines Activity

### Description

THIS weekly discussion WILL CLOSE FOR STUDENT INPUT AT THE END OF THE WEEK as week 7 opens up so be sure to answer or add your own questions.

PROBLEM: Given f(x)=4x – x^{2} + k & (1,3+k) on the graph of f.

Solve if k=6

a) Write you equation after substituting in the value of k.

b) Calculate the function values, showing your calculations, then graph three secant lines

i. One thru P(1,f(1)) to P_{1}(0.5,__)

ii. One thru P(1,f(1)) to P_{2}(1.5,__)

iii. One thru P_{1 }to P_{2}

c) Find the slope of each of these three secant lines showing all calculations.

d) NO DERIVATIVES ALLOWED HERE! Use the results to estimate the slope

of the tangent line at (1,3+k).

e) How would you improve your approximation?

f) Please locate and list an appropriate resource url as a selectable url

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