Question

1. For the function f(x) = x2, Find the slope of the secant line joining (1,f(1)) and

(1.01, f(1.01))

Please solve with an explanation please

Answer 1

The slope of the line connecting two points (a, b) and (c, d) is

(d - b) / (c - a)

i.e. the change in the y-coordinate divided by the change in the x-coordinate. For a function y = f(x), this slope is the slope of the secant line connecting the two points (a, f(a) ) and (c, f(c) ), and has a value of

(f(c) - f(a) ) / (c - a)

Here, we have

f(x) = x ²

so that

f (1) = 1² = 1

f (1.01) = 1.01² = 1.0201

Then the slope of the secant line is

(1.0201 - 1) / (1.01 - 1) = 0.0201 / 0.01 = 2.01