MATH 1ZA3 Lecture 20: Lecture 20
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Solution comes from maximising or minimising some f(x) From "+(+3)"=" and *+,- = *. we saw. *0+12 < a function of 1 variable and find abs. *0+12 easier and find abs min of "(and square roots at end) Look at domain of variables: l>0, x>0, h>0. F"(x)=0 when , 3=0 > when x = 3 3 (cube root) (on x > 0) 1st derivative test: on (0, 3 3) f"(x) < 0 on (3 3@ Example find the point on the parabola =2" 1 that is closest to the point (1/2, 2) Distance (a1, b1) > (a2, b2) h(2 1)+(2 1)" d=kyx 12z"+(2x" 1 2)" > minimise d (or ", if you prefer and remember to at end) Proceed exactly as in ladder problem from here. Example a wire of 50cm is cut into 2 pieces, with one piece made into a square and the other into a circle.
