  For the function​f(x)=-3x^2make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at x=2.Interval [1,2]

Question

For the function

​f(x)=-3x^2

make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at x=2.

Interval [1,2]

Step 1

It is known that the slope of a secant line between points (a, f(a)) and (b, f(b)) is given by:

Step 2

Now, evaluate slopes of secant line at different intervals between the provided interval [1,2]: help_outlineImage Transcriptioncloseat 1,2 -2(9) at 1.5,2 f(2)-(L.5)-12-(-6.75) f(2)-f(1)12-(-3 2-1 1 -5.25 -10.5 2-1.5 0.5 0.5 at [1.9,2 f(2)-f(1.9) 12-(-10.83) -1.17_11.7 2-1.9 0.1 0.1 at 199,2] f (2)-f(1.99)-12-(-11.8803) -0.1197 --11.97 2-1.99 0.01 0.01 [1.999,2 at f(2)-f(1.999)-12-(- 2-1.999 -11.988003)-0.011997 =-11.997 0.001 0.001 fullscreen
Step 3

So, the table of slopes of seca... help_outlineImage TranscriptioncloseInterval [1.9,2] -11.7 [1.999,2] -11.997 [1,2] -9 [1.5,21 -10.5 [1.99,2] -11.97 Slope of secant line fullscreen

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Calculus 