coca a DR RAIA LATTF MATH I422-103FALL 2014. THIRD EXAM ID NO ......002B. DECEMB

Question

coca a DR RAIA LATTF MATH I422-103FALL 2014. THIRD EXAM ID NO ......002B. DECEMBER, 1614.VX02 PAGES6, coDE o01 PG.8 (A) TRUE OR FALSE f (r) is Concave Upward on oo,- v2) (B) TRUE OR FALSE f (r) is Concave Upward on V2, V2) (Ch liRUE OR FALSE f (r) is concave upward on (v2, c) (D) TRUE OR FALSE f(z) is concave Upward on (-v2, 0). (E) TRUE OR FALSE f (z) is Concave Upward on (0, v2) 6Q17. (Marks 5). Let y 3r2 (r 3)3/2 Find the first derivative z 3Q18. Linear Approximation L (a) to the function f(z) near the point z a L(z) f(a) fl (a).(r a) (1 near the point Find the Linear Approximation L(r) to the function L (r)

Explanation / Answer

1) f(x) = 3x^2(x-3)^1.5
dy/dx= 6x(x-3)^1.5 + 4.5x (x-3)^.5
at x=4
we have dy/dx = 24 +18 = 42

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