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