How many critical points does the function f(x)=(x-2)^5(x+3)^4 have?
3 Answers
Three
Explanation:
Recall the product and chain rules. These will help you get the derivative without having to make the lengthy expansion of the function.
•Chain rule: For a function
•Product rule: For a function
Applying these rules:
f'(x) = 5(x - 2)^4(x + 3)^4 + 4(x -2)^5(x + 3)^3
Now we need to let this be
0 = (x - 2)^4(x + 3)^3(5(x + 3) + 4(x- 2))
Thus we have three separate equations:
x -2 = 0
x + 3 = 0
5(x +3) + 4(x- 2) = 0
The solution to the first two equations is immediately visible as being
5(x + 3) + 4(x - 2) = 0
5x + 15 + 4x - 8 = 0
9x = -7
x = -7/9
Therefore, there will be
Hopefully this helps!
Three.
Explanation:
= (x-2)^4(x+3)^3[5(x+3)+4(x-2)]
= (x-2)^4(x+3)^3(9x+7)
Explanation:
If
First we need to find the derivative of
Using product rule:
If
All solution are: