Differentiation: The derivative
The difference quotient at a point
Approach the slope of #f(x)=\frac{1}{4}x^2+3# for #x=2# by calculating the difference quotient of #f# at #2# with difference #h# for successively #h=1#, #h=\frac{1}{10}#, #h=\frac{1}{100}#, #h=\frac{1}{1000}# and #h=\frac{1}{10000}#. Round to #5# decimal places.
The difference quotient for #h=1# is: |
The difference quotient for #h=\frac{1}{10}# is: |
The difference quotient for #h=\frac{1}{100}# is: |
The difference quotient for #h=\frac{1}{1000}# is: |
The difference quotient for #h=\frac{1}{10000}# is: |
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