Use the limit definition of the derivative to find the slope of the tangent line to the curve f ( x ) = 6 x 2 \displaystyle {f{{\left({x}\right)}}}={6}{x}^{{2}} f ( x ) = 6 x 2 x = 4 \displaystyle {x}={4} x = 4
Step 1
f ( 4 + h ) = \displaystyle {f{{\left({4}+{h}\right)}}}= f ( 4 + h ) = Preview Question 6 Part 1 of 5
Step 2
f ( 4 + h ) − f ( 4 ) = \displaystyle {f{{\left({4}+{h}\right)}}}-{f{{\left({4}\right)}}}= f ( 4 + h ) − f ( 4 ) = Preview Question 6 Part 2 of 5
Step 3
f ( 4 + h ) − f ( 4 ) h = \displaystyle \frac{{{f{{\left({4}+{h}\right)}}}-{f{{\left({4}\right)}}}}}{{h}}= h f ( 4 + h ) − f ( 4 ) = Preview Question 6 Part 3 of 5
Step 4
lim h → 0 f ( x + h ) − f ( 4 ) h = \displaystyle \lim_{{{h}\to{0}}}\frac{{{f{{\left({x}+{h}\right)}}}-{f{{\left({4}\right)}}}}}{{h}}= h → 0 lim h f ( x + h ) − f ( 4 ) = Preview Question 6 Part 4 of 5
So, f ′ ( 4 ) = \displaystyle {f}'{\left({4}\right)}= f ′ ( 4 ) = Preview Question 6 Part 5 of 5
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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 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