Question
Asked Sep 28, 2019
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69. Find a cubic function y
graph has horizontal tangents at the points (-2, 6) and
(2, 0).
= ax +bx +cx + d whose
c that ha
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69. Find a cubic function y graph has horizontal tangents at the points (-2, 6) and (2, 0). = ax +bx +cx + d whose c that ha

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Expert Answer

Step 1

The form of cubic function is given as follows.

yax bxx +d
Also given that y(x) have horizontal tangents at (-2,6) and (2,0)
dy
2) = 0
dx
dy2)-0 and
Also y(-2) 6 and y (2) 0.
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yax bxx +d Also given that y(x) have horizontal tangents at (-2,6) and (2,0) dy 2) = 0 dx dy2)-0 and Also y(-2) 6 and y (2) 0.

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Step 2

Obtain the values of unknown as follows.

y axbx cx + d
dy
d
-(ax + bx2 + cx+ d
dx
3
-띠 버음미음이 [
-9-습0금미
d
d
+
dx
d
d
d
(ax)
(bx*)
(cx)+
dx
dx
dx
dx
dx
dx
d
d
(af (x)) a((x))
dx
dx
3ax 2bx ¢
d
nx"-1
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y axbx cx + d dy d -(ax + bx2 + cx+ d dx 3 -띠 버음미음이 [ -9-습0금미 d d + dx d d d (ax) (bx*) (cx)+ dx dx dx dx dx dx d d (af (x)) a((x)) dx dx 3ax 2bx ¢ d nx"-1

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Step 3

Simplify fur...

dy
(-2) 0
dx
3a(-2)+2b(-2)+c =0
12a 4b+c o
.1)
dv
-(2)= 0
dx
3a(2)+2b(2)+c= 0
12a 4b+c 0
(2)
()-(2)
-8b 0
b0
12ac 0
c=-12a
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dy (-2) 0 dx 3a(-2)+2b(-2)+c =0 12a 4b+c o .1) dv -(2)= 0 dx 3a(2)+2b(2)+c= 0 12a 4b+c 0 (2) ()-(2) -8b 0 b0 12ac 0 c=-12a

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Tagged in

Math

Calculus

Functions