Question: We say two curves intersect at right angles if their tangent lines at a point (p,q) are perpendicular. That is, if the slope of one
We say two curves intersect at right angles if their tangent lines at a point (p,q) are perpendicular. That is, if the slope of one curve's tangent line at (p,q) is m, then the slope of the other curve's tangent line at that point is -1m.(a) Find the value of the positive constant C such that y=x2 and y=C-x2 intersect at right angles. (See drawing on the left below.)(b) Find the value of the positive constant D such that y=x2 and y=D2-2Dxx2 intersect at right angles. (See drawing on the right below.)The graphs of f(x) and g(x) are shown to the right, with f as a dotted line and g as a solid line. Let F(x)=(f@g)(x). Find F'(2).(You may have to estimate some valoes. Your estimates don't have to be exact, but do show what your estimates of any needed values are.)
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