The figure shows the curve $y=x^2$ and the point D(-1,0). P(p,0) is a variable point on the x-axis and PQ is parallel to the y-axis. Express the area,A, of the triangle DPQ in terms of p. ?

Question

If p is increasing at the rate of 5 units per second, calculate the rate at which A is increasing at the instant when p=4 unit

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Answer 1 · 2018-06-02T18:18:38

$140 " square units per sec"$

$"Area" = 1/2 " base" times " height$

$A(p)= 1/2(p+1)p^2$

$(dA)/(dt) = (dA)/(dp) * (dp)/(dt) = underbrace((3 p^2 + 2p)/2)\_("at "p = 4) * 5 = 140 " square units per sec"$