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The graph y=f(x) of the function f(x)=p2x4−px3+qx2+px+q, where p,q>0, is concave up over its entire domain.
Show that q>83.
The line L has slope p and x-intercept −23. It is given that L is tangent to the curve of y=f(x).
Show that q=23p.
Given that f′′(p1)=5f′(0), find the value of p and the value of q.
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Consider the line L with slope −m, where m>0, passing through the point (3,5).
Give an expression in terms of m for
(i) the x-intercept of the line,
(ii) the y-intercept of the line.
The line L forms a triangle with the coordinate axes.
Show that the area of this triangle is A=2m9m2+30m+25.
Find the minimum possible area of the triangle.
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