Question
Asked Sep 30, 2019
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on the graph of f(x) = 54x - 2x3 where the tangent line is horizontal
Find the points
(Use symbolic notation and fractions where needed. Give your answer as a comma separated list or ordered pairs in the form
(*, *), (*,*
(, *)...)
(x, y)
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on the graph of f(x) = 54x - 2x3 where the tangent line is horizontal Find the points (Use symbolic notation and fractions where needed. Give your answer as a comma separated list or ordered pairs in the form (*, *), (*,* (, *)...) (x, y)

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Expert Answer

Step 1

Given,

f(x) 54x 2x3
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f(x) 54x 2x3

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Step 2

Here we have to find the points on the graph of f(x) where the tangent is...

So,f'(x d(54x-2x3)
dx
54 — бх2
Since, slope 0
: 54 — бх2 — 0
11
6x2 54
x2 9
When x 3 then f (3) 54 x 3 - 2(3)3 = 108
And when x -3 then f(-3) 54 x (-3) 2-3)3 108
Therefore, the points on the graph of f(x) where the tangent is horizontal are
(3, 108) and (-3, -108)
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So,f'(x d(54x-2x3) dx 54 — бх2 Since, slope 0 : 54 — бх2 — 0 11 6x2 54 x2 9 When x 3 then f (3) 54 x 3 - 2(3)3 = 108 And when x -3 then f(-3) 54 x (-3) 2-3)3 108 Therefore, the points on the graph of f(x) where the tangent is horizontal are (3, 108) and (-3, -108)

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Tagged in

Math

Calculus

Derivative