Given the function below Find the equation of the tangent line to the graph of t

Question

Given the function below Find the equation of the tangent line to the graph of the function at x = 1 - Answer in mx + b form. Use the tangent line to approximate f(1.1). Compute the actual value of f(1.1). What is the error between the function value and the linear approximation? Answer as a positive value only. Enter your answer as an expression. Example: 3x^2+1, x/5, (a + b)/c Be sure your variables match those in the question Enter your answer as a whole or decimal number. Examples: 3, -4: 5.5 Enter DNE for Does Not Exist, oo for Infinity Enter your answer as a whole or decimal number. Examples: 3: -4: 5.5 Enter DNE for Does Not Exist, oo for Infinity

Explanation / Answer

f(1) = 6

dy/dx at (1,6) = (1/3)(180 * 3 * 1^2)(180x^3 + 36)^(-2/3)

= 180/36 = 5

y-6 = 5(x-1)

y = 5x + 1

L(1.1) = f(1) + 5(x - 1)

L(1.1) = 6.5

f(1.1) = 6.5075

Error = 0.0075

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