Questions: The function f(x)=2x^3-36x^2+210x-7 has two critical numbers. The smaller one is x= and the larger one is x=

The function f(x)=2x^3-36x^2+210x-7 has two critical numbers. The smaller one is x= and the larger one is x=
Transcript text: The function $f(x)=2 x^{3}-36 x^{2}+210 x-7$ has two critical numbers. The smaller one is $x=$ $\square$ and the larger one is $x=$ $\square$
failed

Solution

failed
failed

Solution Steps

Step 1: Find the Derivative

To find the critical numbers of the function \( f(x) = 2x^3 - 36x^2 + 210x - 7 \), we first calculate its derivative:

\[ f'(x) = 6x^2 - 72x + 210 \]

Step 2: Set the Derivative to Zero

Next, we set the derivative equal to zero to find the critical points:

\[ 6x^2 - 72x + 210 = 0 \]

Step 3: Solve for Critical Points

By solving the quadratic equation, we find the critical points:

\[ x = 5 \quad \text{and} \quad x = 7 \]

Final Answer

The smaller critical number is \( \boxed{x = 5} \) and the larger critical number is \( \boxed{x = 7} \).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Check on the left (orange) circle and drag until the probability P(A) = 0.07. Make sure the orders on the right (blue) circle is probably a P(B) = 0.07. Make sure the answer is not over 0.07. a. 0.588 b. 0.254 c. 0.025 d. 0.55
failedAnswered
Select a daughter DNA strand from the following original strand. 5' CCATGCATTGGTTAG 3' 3'-GGTACGTAACCAATC-5' 3'-GGTAGGTAAGCAATC-5' 3'-GGTUCGTUUCCUUTC-5' 3'-GGUACGUAACCAAUC-5'
failedAnswered
Sampling by □ is a measurement in the amount of deviation from a set standard.
failedAnswered
Which type of DNA mutation occurs when a base is removed? deletion substitution insertion none of these
failedAnswered
The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point? 454 328 396 379 427 535 339 353 406 451 361 392 380 423 416 311 478 441 513 463 The cutoff point is minutes. (Round to the nearest minute.)