flx) and g (x)we ore given.Con cave down .* f"gu exists.*f' まog'an +0 , 9" Ca $0•f(x) is increa sing.Prove hcx)= fig(x)) is concave do wn

Answered: Image /qna-images/answer/730a1bee-1a23-466e-9f89-f27173c06844.jpg

Answered: we ore given'. f(x) and g Cx) Con cave…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The function f(x) = (5x)* satısfies f'(c) = 0 for which value of c? a) Oc = 5e b) Ос - 0 C. c) O c c= 1 d) O c e) O None of the above.
o'pg. 156-159 J #1.) Determine f' and F", if (x)=x²-14 X4 #2.) For y = x9-7x³ +2, find d²y dx2 #6) Determine the maximum and a f(x) = 2x³-9x², -2≤ x ≤ 4 minimum of each function on the given interval b) f(x) = 12x - x³, x= [-3,5] (²) f(x) = 2x + 18,1 fcx)=x²-2x + 6₁-1 ≤ x ≤7 b) f(x)= x³ + x², -3 ≤ x ≤ 3 Cf(x)= x³-12x + 2,-5 ≤ x ≤ 5 d.) f(x) = 3x5-5x³, -2≤x≤4
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Ofx)=5x"_3x²-Z+t] 4 2 find f6 and fW) (x) f =x* Inx find f') and fe
1) In this problem, let x = 2, the value Ax = dx, dy = f'(x)dx, and Ay = f(x + Ax)-f(x) to complete the table f(x)=√x 1.0000 0.5000 0.1000 0.0100 0.0010 2) dx= Ax dy Ay Ay - dy dy Ay 3) 4) f(x) = 5x √2x+3 Find the first derivative given that dy Find X by implicit differentiation. √√x+y+√√x = 4 dx -лr² h A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at the rate of 10 cubic feet per minute, find the rate of change of the depth of the water the instant it is 8 feet deep? 1 V
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we ore given'. f(x) and g Cx) Con cave down. f" gu exists. *f') キ0 g" Cx) #0 f (x) is increa sing. Prove hcx)= fig(x)) is concave down