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Find the average rate of change of f(x)=−x+17f(x) = -x + 17 between x=2x = 2 and x=2+hx = 2 + h, where h≠0h \neq 0.\newlineSimplify your answer. Your answer may be a number or an expression in terms of hh.

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Q. Find the average rate of change of f(x)=−x+17f(x) = -x + 17 between x=2x = 2 and x=2+hx = 2 + h, where h≠0h \neq 0.\newlineSimplify your answer. Your answer may be a number or an expression in terms of hh.
  1. Identify Function and Points: Identify the function and the points for calculating the average rate of change. f(x)=−x+17f(x) = -x + 17, calculate from x=2x = 2 to x=2+hx = 2 + h.
  2. Find Function Values: Find the function values at x=2x = 2 and x=2+hx = 2 + h.f(2)=−(2)+17=15f(2) = -(2) + 17 = 15,f(2+h)=−(2+h)+17=15−hf(2 + h) = -(2 + h) + 17 = 15 - h.
  3. Calculate Average Rate of Change: Calculate the average rate of change using the formula: [f(x2)−f(x1)]/(x2−x1)[f(x_2) - f(x_1)] / (x_2 - x_1). Here, x1=2x_1 = 2 and x2=2+hx_2 = 2 + h. Average rate of change = [f(2+h)−f(2)]/[(2+h)−2][f(2 + h) - f(2)] / [(2 + h) - 2] = [(15−h)−15]/h[(15 - h) - 15] / h = −h/h-h / h = −1-1.

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