PROBLEM: Given f(x)=4x - x² + k& (1,3+k) on the graph of f. Student 1 --> k=1, Student 2 --> k=2, etc.

REPLACE K WITH ANY NUMBER

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 P₁(0.5,__)

ii. One thru P(1,f(1)) to P₂(1.5,__)

iii. One thru P₁ to P₂

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?