The first derivative of the function f(x) = x² - 5 is equal to f'(x) = 2 · x.
<h3>How to find the derivative of a quadratic equation by definition of derivative</h3>
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
#SPJ1
Answer:
32/9
Step-by-step explanation:
2*(2)(8/9) = 4*8/9 = 32/9
21 / 32 = (3/4) * (1/2) * height
21 / 32 = (3 / 8) * height
21 / 32 * (3 / 8) = height =
63 / 256 inches
Answer:
For the top table:
[x] | 3.1 | 2.5 | 1.2 | 0.9 | 0.14 | 0.06 | 0.02 |
[y] | 15.5 | 12.5 | 6 | 4.5 | 0.7 | 0.3 | 0.1 |
For the bottom table:
k = 5
[x] | 3.1 | 2.5 | 1.2 | 0.9 | 0.14 | 0.06 | 0.02 |
[y] | 15.5 | 12.5 | 6 | 4.5 | 0.7 | 0.3 | 0.1 |
Yes that is correct.Well done!:D
