14 V m/s Consider the function below (a) Find G (a) (b) Use the answer from part

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14 V m/s Consider the function below (a) Find G (a) (b) Use the answer from part (a) to find an equation of the tangent line to the curve y = answer from part (a) to find an equation of the tangent line to the curve y Glo) at the point (2, 28). (c) use the answer from part (a) to find an equation of the tangent line to the curve y - Gx) at the point (3, 54). Find fTa) rTa) - LSubmit Answer Save Progress 0.50.5 points Previous Answers SCalcCC4 26 035 The limit represents the derivative of some function f at some number a. State such an f and lim 4-16

Explanation / Answer

1)

a)

G(x) = 9x^2-x^3

G'(x) = 18x - 3x^2

G'(a) = 18a - 3a^2 Answer

b)

Let equation of tangent be , y=mx+c

Slope at (2,28) , m = 18*2 - 3* 4 = 24

Also,

28 = 24*2 +c

=> c = -20

Therefore,

Tangent : y=24x-20 Answer

c)

Let equation of tangent be , y=mx+c

Slope at (3,54) , m = 18*3 - 3* 9 = 27

Also,

54 = 27*3 +c

=> c = -27

Therefore,

Tangent : y=27x-27 Answer

2)

f(x) = sqrt(1-2x)

Using chain rule,

f '(x) = -2/2sqrt(1-2x) = -1/sqrt(1-2x)

f '(a) = -1/sqrt(1-2a) Answer

3)

lim (x->2) (4^x -16)/(x-2)

This is 0/0 form, So

Using L'Hospitals rule

lim (x->2) 4^x* log2(4) = 16 * log24 = 32

Hence , f(x) =4^x , a=16 Answer

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