Answer:
<h2>-4</h2>
Step-by-step explanation:
Given the function f(x)=(x+4)², <u>the x intercept occurs at f(x) = 0,</u> substituting f(x) = 0 into the given equation to get the value of x we have;
Taking the square root of both sides
Subtracting 4 from both sides of the equation
Therefore the x intercept of the equation is -4
9514 1404 393
Answer:
a^2b^5
Step-by-step explanation:
Anything divided by itself is 1.
That is, anything multiplied by its reciprocal is 1. This value (the reciprocal of the expression) is called the "multiplicative inverse." Its value is that the product of an expression and its multiplicative inverse is 1, the multiplicative identity element. (Anything times 1 is itself.)
So, to get 1 as a product, multiply by 1/(a^2b^5), which is to say, divide by a^2b^5 to get 1 as a quotient.
First, you need to find the derivative of this function. This is done by multiplying the exponent of the variable by the coefficient, and then reducing the exponent by 1.
f'(x)=3x^2-3
Now, set this function equal to 0 to find x-values of the relative max and min.
0=3x^2-3
0=3(x^2-1)
0=3(x+1)(x-1)
x=-1, 1
To determine which is the max and which is the min, plug in values to f'(x) that are greater than and less than each. We will use -2, 0, 2.
f'(-2)=3(-2)^2-3=3(4)-3=12-3=9
f'(0)=3(0)^2-3=3(0)-3=0-3=-3
f'(2)=3(2)^2=3(4)-3=12-3=9
We examine the sign changes to determine whether it is a max or a min. If the sign goes from + to -, then it is a maximum. If it goes from - to +, it is a minimum. Therefore, x=-1 is a relative maximum and x=1 is a relative miminum.
To determine the values of the relative max and min, plug in the x-values to f(x).
f(-1)=(-1)^3-3(-1)+1=-1+3+1=3
f(1)=(1)^3-3(1)+1=1-3+1=-1
Hope this helps!!
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