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Find the average rate of change of k(x)=xk(x) = x 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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Q. Find the average rate of change of k(x)=xk(x) = x 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. Understand formula: First, we need to understand the formula for the average rate of change, which is (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.
  2. Substitute values: Substitute the values into the function k(x)=xk(x) = x. So, k(4)=4k(4) = 4 and k(4+h)=4+hk(4 + h) = 4 + h.
  3. Plug into formula: Plug these values into the average rate of change formula: (4+h)−4(4+h)−4\frac{(4 + h) - 4}{(4 + h) - 4}.
  4. Simplify numerator and denominator: Simplify the numerator and the denominator: h/hh / h.
  5. Cancel out hh: Since h≠0h \neq 0, we can simplify further by canceling out hh in the numerator and denominator, which gives us 11.

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