How do you find the critical points for #f(x)=x^32x^2+3x#?
To find the critical points you first take the derivative using the power:
Now you set it equal to zero and solve:
When you solve it, it will yield complex roots:
These two solutions are your critical numbers.
By signing up, you agree to our Terms of Service and Privacy Policy
To find the critical points of ( f(x) = x^3  2x^2 + 3x ), you need to find the values of ( x ) where the derivative ( f'(x) ) is zero or undefined.

Calculate the derivative ( f'(x) ) of the function ( f(x) ): [ f'(x) = \frac{d}{dx} (x^3  2x^2 + 3x) ] [ f'(x) = 3x^2  4x + 3 ]

Set ( f'(x) ) to zero and solve for ( x ) to find the critical points: [ 3x^2  4x + 3 = 0 ]
This quadratic equation doesn't factor easily, so you can use the quadratic formula: [ x = \frac{b \pm \sqrt{b^2  4ac}}{2a} ] where ( a = 3 ), ( b = 4 ), and ( c = 3 ).
[ x = \frac{(4) \pm \sqrt{(4)^2  4(3)(3)}}{2(3)} ] [ x = \frac{4 \pm \sqrt{16  36}}{6} ] [ x = \frac{4 \pm \sqrt{20}}{6} ] [ x = \frac{4 \pm 2i\sqrt{5}}{6} ]
The critical points for ( f(x) = x^3  2x^2 + 3x ) are the values of ( x ) where ( f'(x) = 0 ), which are: [ x = \frac{4 + 2i\sqrt{5}}{6} ] [ x = \frac{4  2i\sqrt{5}}{6} ]
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 What are the critical values, if any, of #f(x)= x^6ln(x) #?
 How do you find the critical points of #k'(x)=x^33x^218x+40#?
 Given the function #f(x)=x^2+8x17#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [3,6] and find the c?
 What are the extrema and saddle points of #f(x, y) = x^2 + y^2 xy+27/x+27/y#?
 How do you find the number c that satisfies the conclusion of Rolle's Theorem for #f(x) = cos(5x)# for [π/20,7π/20]?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7