Question

If f(x) = x² – 5, evaluate: f(x+h)-f(x)/ h

Answer 1

The first derivative of the function f(x) = x² - 5 is equal to f'(x) = 2 · x.

How to find the derivative of a quadratic equation by definition of derivative

In this question we have a quadratic function, in which we must make use of the definition of derivative to find the expression of its first derivative. Then, the procedure is shown below:

f(x) = x² - 5                                         Given

f' = [(x + h)² - 5 - x² + 5] / h                Definition of derivative

(x² + 2 · x · h + h² - 5 - x² + 5) / h       Perfect square trinomial

(2 · x · h + h²) / h                                Associative, commutative and modulative properties / Existence of additive inverse

2 · x + h                                              Distributive, commutative and associative properties / Definition of division / Existence of multiplicative inverse

2 · x                                                     h = 0 / Result

The first derivative of the function f(x) = x² - 5 is equal to f'(x) = 2 · x.

To learn more on derivatives: brainly.com/question/25324584

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