Let fx5x Use a small interval to estimate f 2 Now improve y

Let f(x)=5^x. Use a small interval to estimate f \' (2). Now improve your accuracy by using an even smaller interval.

f\'(x) = lim (h-->0) [f(x + h) - f(x)]/h. So for small h, we can see that: [f(x + h) - f(x)]/h ˜ f\'(x). Let\'s estimate f\'(2) by using the interval [2, 2.01], then the slope of the secant line will be: f\'(2) ˜ [f(2.01) - f(2)]/(2.01 - 2) = [5^(2.01) - 5^2]/0.01 ˜ 40.5615. If we use the interval [2, 2.001], we see that: f\'(2) ˜ [f(2.001) - f(2)]/(2.001 - 2) = [5^(2.001) - 5^2]/0.001 ˜ 40.2683

$Let f(x)=5^x. Use a small interval to estimate f \' (2). Now improve your accuracy by using an even smaller interval.Solution f\'(x) = lim (h-->0) [f(x + h) - f$

Let fx5x Use a small interval to estimate f 2 Now improve y

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