Answer :
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:
[tex]\frac{\Delta f}{\Delta x} =\frac{f(a+h)-f(a)}{h}[/tex]
For this function f=5x we have:
[tex]f(a)=5a^2\\\\f(a+h)=5(a+h)^2=5a^2+10ah+5h^2[/tex]
Then, we have:
[tex]\frac{\Delta f}{\Delta x} =\frac{f(a+h)-f(a)}{h}=\frac{5a^2-(5a^2+10ah+5h^2)}{h}=-10a+5h[/tex]
The value for a is a=1
For h=1
[tex]\Delta f/\Delta x=-10a-5h=-10-5=-15[/tex]
For h=0.1
[tex]\Delta f/\Delta x=-10-5(0.1)=-10-0.5=-10.5[/tex]
For h=0.01
[tex]\Delta f/\Delta x=-10-5(0.01)=-10-0.05=-10.05[/tex]
For h=0.001
[tex]\Delta f/\Delta x=-10-5(0.001)=-10-0.005=-10.005[/tex]
For h=0.0001
[tex]\Delta f/\Delta x=-10-5(0.0001)=-10-0.0005=-10.0005[/tex]