Given the function
f ( x ) = − 4 x 2 \displaystyle {f{{\left({x}\right)}}}=-{4}{x}^{{2}} f ( x ) = − 4 x 2
Find the difference quotient
f ( x + h ) − f ( x ) h \displaystyle {\frac{{{f{{\left({x}+{h}\right)}}}-{f{{\left({x}\right)}}}}}{{{h}}}} h f ( x + h ) − f ( x ) Preview Question 6 Part 2 of 6
Find
f ′ ( x ) \displaystyle {f}'{\left({x}\right)} f ′ ( x ) by determining
lim h → 0 f ( x + h ) − f ( x ) h \displaystyle \lim_{{{h}\rightarrow{0}}}{\frac{{{f{{\left({x}+{h}\right)}}}-{f{{\left({x}\right)}}}}}{{{h}}}} h → 0 lim h f ( x + h ) − f ( x ) .
Preview Question 6 Part 3 of 6
Find
f ′ ( − 2 ) \displaystyle {f}'{\left(-{2}\right)} f ′ ( − 2 ) Preview Question 6 Part 4 of 6
Find
f ′ ( 0 ) \displaystyle {f}'{\left({0}\right)} f ′ ( 0 ) Preview Question 6 Part 5 of 6
Find
f ′ ( 1 ) \displaystyle {f}'{\left({1}\right)} f ′ ( 1 ) Preview Question 6 Part 6 of 6
Graph the function
f ( x ) = − 4 x 2 \displaystyle {f{{\left({x}\right)}}}=-{4}{x}^{{2}} f ( x ) = − 4 x 2 and draw the tangent lines to the graph at points whose x-coordinates are -2 , 0, and 1. (The slopes of these lines should match the derivative values you calculated above.)
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Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
