Use the following function to complete parts a. through d f(x) = m2; a = 1; f(1.

Question

Use the following function to complete parts a. through d f(x) = m2; a = 1; f(1.2) a. Write the equation of the line that represents the linear approximation to the given function at the given point a (Use integers or fractions for any numbers in the expression.) b. Graph the function and the linear approximation near x-a. Select the correct graph below. f(x) fx)X c. Use the linear approximation to estimate the given function value f(1.2)(Round to three decimal places as needed.) approx - exact exact d. Compute the percent error in the approximation: 100 The percent error is %. (Round to three decimal places as needed.)

Explanation / Answer

f(x)= x(x+2)

f(1)= 1/(1+2)=1/3

f'(x)= 2/(x+2)2

at a=1 , f'(x)= 2/9

f(x)= L(x)= f(a)+f'(a)(x-a) = (1/3)+(2/9)(x-1)=(2x/9)+(1/9)

c. f(1.2)= (2*1.2/9)+(1/9)=0.378

d.Exact value of f(1.2)= 1.2/(1.2+2)= 0.375

Percent error= | 0.378-0.375|*100/0.375=0.8%

Correct graph is c.

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