for f(x)=ax^2+bx^3, what is the ordered pair (a,b) if the point (-1,2) is an extrema of f(x)
Mathematics · Middle School · Tue Nov 03 2020
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Given the function:
f(x)=ax^2+bx^3, what is the ordered pair (a,b) if the point (-1,2)
Find the extrema.
Solution:
In order to find extrema of a function, we must first take its first derivative. Derivative can be written as y' or f'(x) read as y prime or f prime of x or derivative of x
f(x)=ax^2+bx^3
f'(x) = 2ax + 3bx^2
In order to find the derivative of the given function, we multiply the degree with the term, and the degree of the function will be subtracted by 1. For such instance ax^2 became 2ax , and bx^3 became 3bx^2
Now we plug in the given points. (-1,2)
f'(-1,2) = 2(-1)x +3(2)x^
f'(-1 2) = -2x + 6x^2
Noticed that the function is factorable by -2x.
= -2x( 1+ 3x)
Solve for x.
1+3x = 0
3x = -1
x = -⅓
-2x = 0
x = 0
The extrema of the given function are x = -⅓ and x= 0