What is the maximum number of possible extreme values for the function, F(x)=x^3-7x-6
2 answers:
Answer:
The maximum number of possible extreme values for the function,
is:
2
Step-by-step explanation:
By the Theorem of extreme values of a polynomial function we have:
The graph of a polynomial equation of degree n has atmost ( less than or equal to) "n-1" extreme values ( i.e. minima and/or maxima).
That means the total number of extreme values could be n-1, n-3, n-5 etc.
Hence, here we have a polynomial equation as:
i.e. we have a polynomial function of degree 3 i.e. n=3
So, the maximum number of possible extreme values that may exits is: 2
( Since n-1=3-1=2)
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Step-by-step explanation:
This seems to be calculus 1.
<u>Question a</u>
We have
m = slope = derivative
Find the derivative / slope of
We do this by differentiating the polynomials. There are a few methods to do this but I am going to use the power rule, which we multiply the constant by the exponent on the variable and subtract one from the exponent.
when x = a
<em>Now that we have this information, we can answer question b</em>
<u>Question b</u>
<u>The tangent line for Point (1, 12)</u>
First find the slope by using our derivative.
Now that we have our slope, use point slope form to find our tangent line
<u>Now lets do the same for the Point (2, 13)</u>
Find the slope at the point.
Now find the tangent line using point slope form of a line.
Now graph the lines, which I have done and you can see by viewing the image I have attached.
