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Find the average rate of change of k(x)=3xk(x) = 3x between x=−4x = -4 and x=−4+hx = -4 + 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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Average rate of change IIright chevron icon

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Q. Find the average rate of change of k(x)=3xk(x) = 3x between x=−4x = -4 and x=−4+hx = -4 + h, where h≠0h \neq 0.\newlineSimplify your answer. Your answer may be a number or an expression in terms of hh.
  1. Calculate k(x)k(x): Calculate k(x)k(x) at x=−4x = -4 and x=−4+hx = -4 + h.\newlinek(−4)=3(−4)=−12k(-4) = 3(-4) = -12\newlinek(−4+h)=3(−4+h)=3(−4)+3h=−12+3hk(-4 + h) = 3(-4 + h) = 3(-4) + 3h = -12 + 3h
  2. Find average rate: Find the average rate of change using the formula: (k(x2)−k(x1))/(x2−x1)(k(x_2) - k(x_1)) / (x_2 - x_1). Here, x1=−4x_1 = -4 and x2=−4+hx_2 = -4 + h. Average rate of change = (k(−4+h)−k(−4))/((−4+h)−(−4))(k(-4 + h) - k(-4)) / ((-4 + h) - (-4)) = (−12+3h−(−12))/(h)(-12 + 3h - (-12)) / (h) = (3h)/h(3h) / h
  3. Simplify expression: Simplify the expression.\newlineAverage rate of change = 33

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