Derivatives. Suppose that f(1) equals 4 and that f’(1) is equal to 3. A) What is

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Derivatives. Suppose that f(1) equals 4 and that f’(1) is equal to 3. A) What is the approximate value of f(1.05)?
Suppose that g(x)= (f(x))^3 B) what are the values of g(x) and dg/dx when x is equal to 1?
Using the tangent line approximation for g(x) find the approximate value of g(1.05)
50-4 points Suppose that f (1) equals 4 and that f'(1) is equal to 3. What is the approximate value of f (1.05)? Approx. value of f (1.05): Suppose that g (x) = (f (x))3 What are the values of g (T) and dr when x is equal to 17 Value of g (x), dg dg Value of dx: Using the tangent line approximation for g(x), find the approximate value of g(1.05) Approx. value of g (1.05)PL For this question, your answers must be correct to two decimal places. Submit Answer Save Progress Submit Assignment Save As Home My Assign

Explanation / Answer

5)

f(1.05) f(1) +(f '(1))*(1.05-1)

=> f(1.05) 4 +(3)*(1.05-1)

=> f(1.05) 4 +(3*0.05)

=> f(1.05) 4 +0.15

=> f(1.05) 4.15

approx.value of f(1.05) is 4.15

g(x)=(f(x))3

g(1)=(f(1))3

=>g(1)=43

=>g(1)=64

g(x)=(f(x))3

dg/dx=3(f(x))2(f '(x))

at x =1,

dg/dx=3(f(1))2(f '(1))

dg/dx=3(4)2(3)

dg/dx=144

g(1.05)=g(1) +(dg/dx)*(1.05-1)

g(1.05)=64 +(144)*(1.05-1)

g(1.05)=71.2

approx.value of g(1.05) is 71.2

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