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.
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The negative solution is x = –1.
Solution:
Let the number be x.
Square of a number = x²
3 times a number = 3x
Difference of square of a number and 4 = 3 times that number
Subtract 3x from both sides of the equation, we get
–3x can be written as x – 4x.
1st bracket have common term x and bracket have –4 common term.
Take common term x + 1 outside.
<em>By zero factor principle, if AB = 0 then A = 0 or B = 0.</em>
x + 1 = 0, x – 4 = 0
x = –1, x = 4
The negative solution is x = –1.
Answer is:
a) 32
b) 59
Both are arithmetic sequences
Answer:
8 chairs
Good Info:
You have 5 quarts of paint
It takes 5/8 quarts for 1 chair
Step-by-step explanation:
So, do 5 divided by 5/8=8
To check this, do 5 times 5/8.
Multiples of 5/8:
5/8
1 2/8 or 1 1/4
1 7/8
2 4/8 or 1 2/4 or 1 1/2
3 1/8
3 6/8 or 3 3/4
4 3/8
5
What do u want me to do?
They are in Fraction form
