How do you find the slope of the

Harrison Reeves

Harrison Reeves

Answered question

2022-04-12

How do you find the slope of the secant lines of y=2x2+sec(x) at x=0 and x=π?

Answer & Explanation

jchordig1d5

jchordig1d5

Beginner2022-04-13Added 7 answers

The secant line between two points on a curve (there is only one such line), is the straight line between the two points on the curve.
The two points here are:
x1=0
y1=202+sec(0)=0+1cos(0)=1,
and
x2=π
y1=2π2+sec(π)=2π2+1cos(π)=2π21
The slope k of a straight non-vertical line is given by the formula
k=y2y1x2x1=2π211π0=2π22π,
which in this case is the slope of the sought secant line.

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