CALCULUS help please ill give u ten points if u give me the correct answers…?
2)The x-value where the function f(x)=x^9 * e^(-12x^2) has a relative maximum.
3)Find the x-value of all the points where the function f(x)=
-(2 – 6x) ^(2/3), has any relative extrema. Then find the values of any extrema.
4)Find the x-value of all poits where the function f(x)= 6x^3 +44x^2 -10x +9, has any realtive extrema
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1) I suppose you mean f(x) = (x+9)/(x+3)? Parentheses are very important. The way you have it typed actually means
f(x) = x + (9/x) + 3.
f(x) = (x+9)/(x+3)
Take the derivative using the Quotient Rule.
f'(x) = [(x+3)(1) – (x+9)(1)] / (x+3)^2
Simplify
f'(x) = (x + 3 – x – 9)/(x+3)^2
f'(x) = -6/(x+3)^2
Critical points occur whenever the numerator or denominator equals zero.
-6 never equals zero, so you will not have any relative extrema.
(x+3)^2 = o when x = -3
This gives you two intervals: (-infinity, -3) and (-3, infinity)
Pick a test point in each interval and check to see if f'(x) is positive or negative.
In this case you will see that f'(x) is negative on both intervals.
Therefore, f(x) is decreasing on the intervals (-infinity,-3)U(-3,infinity)
