Graph the function f(x)=−4x2\displaystyle {f{{\left({x}\right)}}}=-{4}{x}^{{2}} and draw the tangent lines to the graph at points whose x-coordinates are -2 , 0, and 1.
Clear All Draw: LineParabola


Find the difference quotient f(x+h)−f(x)h\displaystyle {\frac{{{f{{\left({x}+{h}\right)}}}-{f{{\left({x}\right)}}}}}{{{h}}}}  

Find f′(x)\displaystyle {f}'{\left({x}\right)} by determining lim⁡h→0f(x+h)−f(x)h\displaystyle \lim_{{{h}\rightarrow{0}}}{\frac{{{f{{\left({x}+{h}\right)}}}-{f{{\left({x}\right)}}}}}{{{h}}}}.  

Find f′(−2)\displaystyle {f}'{\left(-{2}\right)} (This slope should match the tangent line you drew above.)
 

Find f′(0)\displaystyle {f}'{\left({0}\right)}  

Find f′(1)\displaystyle {f}'{\left({1}\right)}  

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