Differentiation, derivatives and Taylor approximations: Tangent line
Difference quotient in a point
- Calculate the difference quotient of the function \(f(x)=x^2\) over the interval \([2,2+h]\) for an indeterminate \(h>0\).
- What does the expression found in part (a) become when \(h\) gets negligibly small?
- Calculate the difference quotient of the function \(f(x)=x^2\) over the interval \([2-h,2]\) for an indeterminate \(h>0\).
- What does the expression found in part (c) become when \(h\) gets negligibly small?
| \(\frac{{\vartriangle}f}{{\vartriangle}x}\) over \([2,2+h]={}\) |
| \(\frac{{\vartriangle}f}{{\vartriangle}x}\) over \([2,2+h]\approx{} \) | when \(h\approx 0\). |
| \(\frac{{\vartriangle}f}{{\vartriangle}x}\) over \([2-h,2]={}\) |
| \(\frac{{\vartriangle}f}{{\vartriangle}x}\) over \([2-h,2]\approx{} \) | when \(h\approx 0\). |
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