The extension, e, of a spring is proportional to the mass, m, hung from the spring. A mass of 2kg gives an extension of 5cm.
(a) Find the relationship between e and m.
(b) Use this relationship to find the mass needed to give an extension of 40mm

Hooke's law is a linear relationship

Step-by-step explanation:

Because Hooke's law is linear, we expect that if we double the mass hanging on a spring, the length of the spring will double.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.