# How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = x^3 - 2x^2 - x +1#?

Find and test the critical numbers, then find

By signing up, you agree to our Terms of Service and Privacy Policy

To find the exact relative maximum and minimum of the polynomial function ( f(x) = x^3 - 2x^2 - x +1 ), follow these steps:

- Find the critical points by taking the derivative of the function and setting it equal to zero.
- Determine the intervals where the function is increasing or decreasing using the first derivative test.
- Use the second derivative test to classify the critical points as relative maximums, relative minimums, or points of inflection.

Let's find the critical points first:

( f'(x) = 3x^2 - 4x - 1 )

Setting ( f'(x) ) equal to zero and solving for ( x ):

( 3x^2 - 4x - 1 = 0 )

The solutions for ( x ) will give the critical points.

Next, determine the intervals of increase and decrease by analyzing the sign of ( f'(x) ) in these intervals.

Finally, use the second derivative test on the critical points to determine whether they correspond to relative maximums, relative minimums, or points of inflection.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided 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 one-sided 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 one-sided 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.

- How do you graph of the function #y=arctan(x)#?
- Are the inflection points where f'(x) = zero or where the graph changes from concave up to concave down?
- What is the second derivative of #f(x)= 2x^3- sqrt(4-x^2)#?
- How do you find the inflection point(s) of the following equation #(1+ln(x))^3#?
- How do you find points of inflection of the function function #h(x) = −x^4 + x^2 − 1#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7