Determine where a function has a horizontal tangentQuestion10x313x2Find all the value(s) of x at which f(x) =answer, give all of the x-values separated by commas, e.g. if f (x) has a horizontal tangent line at x = 3 and x = 5 enter 3, 5.+ 4x + 16 has a horizontal tangent line. If there is more than one3

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Asked Dec 4, 2019
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Determine where a function has a horizontal tangent
Question
10x3
13x2
Find all the value(s) of x at which f(x) =
answer, give all of the x-values separated by commas, e.g. if f (x) has a horizontal tangent line at x = 3 and x = 5 enter 3, 5.
+ 4x + 16 has a horizontal tangent line. If there is more than one
3
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Determine where a function has a horizontal tangent Question 10x3 13x2 Find all the value(s) of x at which f(x) = answer, give all of the x-values separated by commas, e.g. if f (x) has a horizontal tangent line at x = 3 and x = 5 enter 3, 5. + 4x + 16 has a horizontal tangent line. If there is more than one 3

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Expert Answer

Step 1

Given:

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10x3 13x2 f(x)= 3 -+4x+16 2

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Step 2

Calculation:

To find the value of in the horizontal tangent line.

For that, we have find the derivative of given function and set equal to zero.

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10х3 13х2 (x)= 3 +4x+16 2 d 10 13 S(x)=(3x)+ (2x)+4 using(x"), = nx"-1 2 dx f'(x)= 10x2 13x+4

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Step 3
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Set f'(x)0, we get 10x213x4=0 10x25x8x4 0 5x(2x+1)+4(2x+1 = 0 (2x+1)(5x +4) 0 by zero product rule, 2x+10 or 5x +4= 0 2x 5 4 1 х- х 2 -4 5

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Tagged in

Math

Calculus

Derivative