Let f(x)=x^(3)-8x. Calculate the difference quotient (f(3+h)-f(3))/h for
h=0.1
h=0.01
h=-0.01
h=-0.1?
If someone now told you that the derivative (slope of the tangent line to the graph) of f(x) at x=3 was an integer, what would you expect it to be?
h=0.1
h=0.01
h=-0.01
h=-0.1?
If someone now told you that the derivative (slope of the tangent line to the graph) of f(x) at x=3 was an integer, what would you expect it to be?
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for the first part of the question.
just have to substitute the (3+h) and 3 for x in the function
f(h)=[(3+h)^3-8(3+h)-(3^3)+8(3)]/h
simplify
f(h)=[(3+h)^3-8(3+h)-3]/h
just plug in the h values and you will see that as the h's approach 0 you will get the derivative at 3.
if you are told the derivative is an integer you can guess the nearest integer will be the derivative.
just have to substitute the (3+h) and 3 for x in the function
f(h)=[(3+h)^3-8(3+h)-(3^3)+8(3)]/h
simplify
f(h)=[(3+h)^3-8(3+h)-3]/h
just plug in the h values and you will see that as the h's approach 0 you will get the derivative at 3.
if you are told the derivative is an integer you can guess the nearest integer will be the derivative.