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Find the average rate of change of f(x)=−10x2f(x) = -10x^2 between x=0x = 0 and x=hx = 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 f(x)=−10x2f(x) = -10x^2 between x=0x = 0 and x=hx = 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 points for calculating the average rate of change.\newlineFunction: f(x)=−10x2f(x) = -10x^2\newlinePoints: x=0x = 0 and x=hx = h
  2. Calculate f(0)f(0) and f(h)f(h): Calculate f(0)f(0) and f(h)f(h).
    f(0)=−10(0)2=0f(0) = -10(0)^2 = 0
    f(h)=−10(h)2=−10h2f(h) = -10(h)^2 = -10h^2
  3. Use Average Rate of Change Formula: Use the formula for average rate of change: (f(b)−f(a))/(b−a)(f(b) - f(a)) / (b - a). Substitute a=0a = 0, b=hb = h, f(0)=0f(0) = 0, and f(h)=−10h2f(h) = -10h^2. Average rate of change = (f(h)−f(0))/(h−0)=(−10h2−0)/h(f(h) - f(0)) / (h - 0) = (-10h^2 - 0) / h
  4. Simplify the Expression: Simplify the expression.\newlineAverage rate of change = −10h2h=−10h\frac{-10h^2}{h} = -10h

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