Question

Given f(x)=3x^2+5

a) find the slope of the secant passing through x=2 and x=4

b) estimate the slope of the tangent at x=4

Answer 1

(a) That would be (f(4)-f(2))/(4-2) = (53-17)/2 = 18

(b) One estimate would be
(f(4.1)-f(3.9))/(4.1-3.9) = (55.43-50.63)/0.2 = 24
(actual slope = 6x = 24)