Need help with a Calculus question

Question

Below is the whole question. All of the data in "a.)" is correct. I need help finding the slope of the tangent line at P (3, 2.8). This is part "b" in bold below.

The experimental data in the table below define y as a function of x

X= 0 1 2 3 4 5

Y= 3.7 2.7 2.5 2.8 3.3 4.3

a.) Let P be the point (3,2.8). Complete the table below by computing the slope of the secant line PQ when Q is the point of the graph with x-coordinate x1

If x1=0, the slope of PQ is: -0.3

If x1=1, the slope of PQ is: 0.05

If x1=2, the slope of PQ is: 0.3

If x1=4, the slope of PQ is: 0.5

If x1=5, the slope of PQ is: 0.75

b.) Draw the graph of the function for yourself and estimate the slope of the tangent line at P(3,2.8)

Answer 1

The data for the slopes of those secants are symmetrical across x = 3. If it were consistent with that pattern of slopes, the slope of the tangent line to the curve at x = 3 should be exactly halfway between the secant slopes at x = 2 and x = 4, which would mean the slope of the line tangent to the curve at P would = .4.