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There is a line through the origin that divides the region bounded by the parabola y = 4 x - 2 x^2 and the x-axis into two regions with equal area. What is the slope of that line?

an olympic athlete ingests an illegal substance at 10:00 pm Friday evening. The amount of the substance in the athlete's body after t hours is determined by the function f(t)=100-30ln(1+t). If...

the derivative or the slope to the function or the function for the tangent line is -2x, using the power rule....however  I understand that first(1,2) and (x,4-x^2) are similar..i.e if...

I need to see the steps for solving the following equation:  Find the equation of the tangent line to the curve at the given points for y=x^2-1/x^2+x+1  (1,0).  I know the answer...

The graphs of the polar curves r=3 and r=4-2sin(theta) are shown in the figure above. The curves intersect when theta=pi/6 and theta=5pi/6.   a) Let S be the shaded region that is inside...

What can you conclude about the graph of f(x) from the following table? justify your answer                          -1  ...

Find the maximum value M and the minimum value m of the function in the given interval use sign charts to support your findings A) y=2 radical x- 3x ;[1,4] B)y=cube root of x+1 + the cube...