find the y coordinates of each stationary points f(0). f(x)=x^3-3x^2-24x-7
I don't know why you wrote f(0). f(0) has nothing to do with stationary points and its value is -7. See my other answer for the x values at the stationary points, and use those two x values to calculate the corresponding y = f(x) values
Well, y is the same as f(x). In other words, y = f(x) and f(x) = y because they are interchangeable.
For example, y = x + 5 is the same as if you were to write it f(x) = x + 5.
Did you know that?
Do you see f(0)?
It tells you to replace x with 0 everywhere you see the letter x and then simplify.
Find y or f(x)when x = 0.
f(x)= x^3 -3x^2 - 24x -7
f(0) = (0)^3 - 3(0)^2 - 24(0) - 7
f(0) = 0 - 0 - 0 - 7
f(0) = -7
The y coordinate is -7 and the entire point is (0, -7).
Is this what you want?
To find the y-coordinate of a stationary point of a function, we need to find the value of the function at that point.
Given the function f(x) = x^3 - 3x^2 - 24x - 7, we can find the stationary points by finding the values of x where the derivative of the function is equal to zero.
Step 1: Find the derivative of f(x):
f'(x) = 3x^2 - 6x - 24
Step 2: Set the derivative equal to zero and solve for x:
3x^2 - 6x - 24 = 0
Step 3: Factor the quadratic equation:
3(x^2 - 2x - 8) = 0
3(x - 4)(x + 2) = 0
Using the zero product property, we have:
x - 4 = 0 or x + 2 = 0
Solving these equations gives us:
x = 4 or x = -2
These are the x-coordinates of the stationary points of the function.
Step 4: Substitute the x-values into the original function to find the corresponding y-values:
For x = 4:
f(4) = (4)^3 - 3(4)^2 - 24(4) - 7
= 64 - 48 - 96 - 7
= -87
For x = -2:
f(-2) = (-2)^3 - 3(-2)^2 - 24(-2) - 7
= -8 - 12 + 48 - 7
= 21
Therefore, the y-coordinates of the stationary points are f(4) = -87 and f(-2) = 21.