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Physics197
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Derivative Question [uhhhhhh.. Help?]
Hopefully you can imagine this:
the line L is tangent to the graph of y=1/x^2 at point P, with coordinates (w,1/w^2), where w > 0. Point Q has coordinates (w,0) [below point P on the x-axis]. Line L crosses the x-axis at point R with coordinates of (k,0).
a) Find the value of k when w=4 [solved!]
b) For all w>0, show that k = 1.5w [Solved]
c) Suppose that w is increasing at the constant rate of 2 units per second. When t=0s, w=1. Draw the graph at t=0s and another at t=3s. Include the tangent line L and label the coordinates of P,Q, R.
>>When it says draw the graph at t=0s and at T=3s, do you draw the graph y=1/x^2 at point (w, 1/w^2) ?
d) What was the average rate of change of k from t=0s to t=3s. Is this a constant rate? Explain.
>>Wouldn't the rate be constant because t is constant, and w is constant, and k=1.5w which would be linear and since w is constant so would k?
e) Suppose that w is increasing at the constant rate of 2 units per second. When t=3s, what is the rate of change of the area of the triangle PQR with respect to time? (Hint: use implicit differentiation with respect to time).
>>Lost here, may come together if I get the previous questions, but I was thinking find the area of the triangle in terms of w and then find the derviative because w' = 2 [rate of change given] and at t=3s, w=7.
Hopefully you can imagine this:
the line L is tangent to the graph of y=1/x^2 at point P, with coordinates (w,1/w^2), where w > 0. Point Q has coordinates (w,0) [below point P on the x-axis]. Line L crosses the x-axis at point R with coordinates of (k,0).
a) Find the value of k when w=4 [solved!]
b) For all w>0, show that k = 1.5w [Solved]
c) Suppose that w is increasing at the constant rate of 2 units per second. When t=0s, w=1. Draw the graph at t=0s and another at t=3s. Include the tangent line L and label the coordinates of P,Q, R.
>>When it says draw the graph at t=0s and at T=3s, do you draw the graph y=1/x^2 at point (w, 1/w^2) ?
d) What was the average rate of change of k from t=0s to t=3s. Is this a constant rate? Explain.
>>Wouldn't the rate be constant because t is constant, and w is constant, and k=1.5w which would be linear and since w is constant so would k?
e) Suppose that w is increasing at the constant rate of 2 units per second. When t=3s, what is the rate of change of the area of the triangle PQR with respect to time? (Hint: use implicit differentiation with respect to time).
>>Lost here, may come together if I get the previous questions, but I was thinking find the area of the triangle in terms of w and then find the derviative because w' = 2 [rate of change given] and at t=3s, w=7.