Answer:h=1 df/dx=-15
h=0.1 df/dx=-10.5
h=0.01 df/dx=-10.05
h=0.001 df/dx=-10.005
h=0.0001 df/dx=-10.0005
Step-by-step explanation: The function should be 5x^2.
If the function is linear, the answer is very simple: it is 5 for every value of h.
The rate of change can be defined as:
\frac{\Delta f}{\Delta x} =\frac{f(a+h)-f(a)}{h}
For this function f=5x we have:
f(a)=5a^2\\\\f(a+h)=5(a+h)^2=5a^2+10ah+5h^2
Then, we have:
\frac{\Delta f}{\Delta x} =\frac{f(a+h)-f(a)}{h}=\frac{5a^2-(5a^2+10ah+5h^2)}{h}=-10a+5h
The value for a is a=1
For h=1
\Delta f/\Delta x=-10a-5h=-10-5=-15
For h=0.1
\Delta f/\Delta x=-10-5(0.1)=-10-0.5=-10.5
For h=0.01
\Delta f/\Delta x=-10-5(0.01)=-10-0.05=-10.05
For h=0.001
\Delta f/\Delta x=-10-5(0.001)=-10-0.005=-10.005
For h=0.0001
\Delta f/\Delta x=-10-5(0.0001)=-10-0.0005=-10.0005
