`What is the formula for finding the critical points of a function in calculus`

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

To find the critical points of the function $f(x) = x^3 - 3x + 1$, we first need to find its derivative

step 2

The derivative of $f(x)$ is $f'(x) = 3x^2 - 3$

step 3

Set the derivative equal to zero to find the critical points: $3x^2 - 3 = 0$

step 4

Solve the equation $3x^2 - 3 = 0$ for $x$

step 5

Divide both sides by 3 to get $x^2 - 1 = 0$

step 6

Factor the equation: $(x - 1)(x + 1) = 0$

step 7

Solve for $x$: $x = 1$ and $x = -1$

Answer

The critical points of the function $f(x) = x^3 - 3x + 1$ are $x = 1$ and $x = -1$.

Key Concept

Critical Points

Explanation

Critical points of a function occur where its derivative is zero or undefined. In this case, the derivative $f'(x) = 3x^2 - 3$ is set to zero and solved for $x$.

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