Introduction to differentiation: Definition of differentiation
The notion of derivative
Below you see the graph #f(x)=\frac{1}{2}x^2+4# and the tangent line #l# at the point #\rv{2,6.00000}#.
Approximate the slope of #l# at the point #\rv{2,6.00000}# by calculating the difference quotient of #f# at #2# with difference #h# for #h=1#, #h=\frac{1}{10}#, #h=\frac{1}{100}#, #h=\frac{1}{1000}#, and #h=\frac{1}{10000}#, respectively. Give your answer to #5# decimal places.
Approximate the slope of #l# at the point #\rv{2,6.00000}# by calculating the difference quotient of #f# at #2# with difference #h# for #h=1#, #h=\frac{1}{10}#, #h=\frac{1}{100}#, #h=\frac{1}{1000}#, and #h=\frac{1}{10000}#, respectively. Give your answer 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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