Use the limit definition to compute the derivative of the function f(x) = 21x3 at x = 1.(Give your answer as a whole or exact number.)f'(1)Find anequation of the tangent line to the graph of f at x = 1.(Use symbolic notation and fractions where needed. Let y =f(x). Express equation in terms of variables x and y.)equation

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Asked Sep 30, 2019
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Use the limit definition to compute the derivative of the function f(x) = 21x3 at x = 1.
(Give your answer as a whole or exact number.)
f'(1)
Find an
equation of the tangent line to the graph of f at x = 1.
(Use symbolic notation and fractions where needed. Let y =
f(x). Express equation in terms of variables x and y.)
equation
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Use the limit definition to compute the derivative of the function f(x) = 21x3 at x = 1. (Give your answer as a whole or exact number.) f'(1) Find an equation of the tangent line to the graph of f at x = 1. (Use symbolic notation and fractions where needed. Let y = f(x). Express equation in terms of variables x and y.) equation

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Expert Answer

Step 1

We use the definition of limit to find the derivative. 

Answer(a): f'(1)=63

f(1+h)-f()
lim
h 0
21(1+h)3-21(1
= lim
h 0
21[(1+h)-(1'
= lim
h
h0
[(1+h)-(1)
=21 lim
h-0
1+3h+3h2+h3-1
21 lim
h- 0
3h+3h2+h3
=21 lim
h
h- 0
-21 lim (3+3h+h2)
h-0
21(3+3(0)+02)
21(3)
=63
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f(1+h)-f() lim h 0 21(1+h)3-21(1 = lim h 0 21[(1+h)-(1' = lim h h0 [(1+h)-(1) =21 lim h-0 1+3h+3h2+h3-1 21 lim h- 0 3h+3h2+h3 =21 lim h h- 0 -21 lim (3+3h+h2) h-0 21(3+3(0)+02) 21(3) =63

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Step 2

At x=1 we have to find...

У-21x3
Оr, y321(1)*
Or, y 21
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У-21x3 Оr, y321(1)* Or, y 21

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