Question

given the function f(x)= x^3+3x find the rate of chnge between the two values x:1 to 2

find the equation of a secant line containing the given points (1,f(1) and (2,f(2))

Answer 1

f(1) = 4
f(2) = 14
rate of change = (14-4)/(2-1) = 10

the slope of the secant is 10, (see above)

equation is y = 10x + b
but (1,4) lies on it, so
4 = 10(1) + b
b = -6

secant equation: y = 10x - 6