Suppose f is differentiable on (-∞,∞) and f(5.01) - f(5) = 0.25.Use linear approximation to estimate the value of f'(5).

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1. Recall the formula for linear approximation, which states that for a function f that is differentiable at a point a, the linear approximation at a is given by f(x) ≈ f(a) + f'(a)(x - a).
2. In this problem, we can set a = 5 and x = 5.01, so we need to express f(5.01) in terms of f(5) and f'(5).
3. Using the linear approximation formula, we can write f(5.01) ≈ f(5) + f'(5)(5.01 - 5).
4. Substituting the known values into the equation, we have f(5.01) - f(5) = f'(5)(0.01).
5. Since we know that f(5.01) - f(5) = 0.25, we can set up the equation 0.25 = f'(5)(0.01) and solve for f'(5).