Sorry for so many questions, I'm just trying to understand everything before my test coming up soon.(adsbygoogle = window.adsbygoogle || []).push({});

1. Let R be the region in the first quadrant under the graph of y=1/sqrt(x) for

4<=x<=9.

a) If the line x=k divides the region R into two regions of equal area, what is the value of k?

My thoughts: For this one, I know how to find the area of R, but I don't know how to start finding the line that divides the region into multiple parts of equal area.

2. Let f be a function given by f(x)=x^3 - 6x^2 + p, where p is an arbitrary constant.

a) Write an expression for f '(x) and use it to find the relative maximum and minimum values of f in terms of p. Show the analysis that leads to your conclusion.

My thoughts: f '(x) = 3x^2 - 12x. Setting this equal to 0 and solving for x gives: x=0, 4. These are critical points, and I know that to find max/min points I need to look at second derivative. But here it says just use first derivative? I'm also not sure what to write for analysis part.

b) For what values of the constant p does f have 3 distinct real roots?

I don't have any thoughts on this one

c) Find the value of p such that the average value of f over the closed interval [-1, 2] is 1.

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# Several calculus problems

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