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Find the average rate of change of g(x)=−3x+8g(x) = -3x + 8 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 g(x)=−3x+8g(x) = -3x + 8 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. Calculate g(x)g(x): Calculate g(x)g(x) at x=2x = 2.\newlineg(2)=−3(2)+8=−6+8=2g(2) = -3(2) + 8 = -6 + 8 = 2.
  2. Calculate g(x+h)g(x+h): Calculate g(x)g(x) at x=2+hx = 2 + h.\newlineg(2+h)=−3(2+h)+8=−6−3h+8=2−3hg(2 + h) = -3(2 + h) + 8 = -6 - 3h + 8 = 2 - 3h.
  3. Find average rate of change: Find the average rate of change using the formula: [g(x2)−g(x1)]/(x2−x1)[g(x_2) - g(x_1)] / (x_2 - x_1).\newlineHere, x1=2x_1 = 2 and x2=2+hx_2 = 2 + h.\newlineAverage rate of change = [g(2+h)−g(2)]/[(2+h)−2]=[(2−3h)−2]/h=(−3h)/h=−3[g(2 + h) - g(2)] / [(2 + h) - 2] = [(2 - 3h) - 2] / h = (-3h) / h = -3.

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