Determine the points on a function when tangent lines have a given slopeQuestion16x3- 4x2 6x - 13 have a tangent line of slope 5?For which value(s) of x does f(x) =3If there is more than one answer, give all of the x-values separated by commas, e.g. if f (x) has a tangent line of slope 5 atx = 3 and x = 5 enter 3, 5.

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Asked Dec 4, 2019
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Determine the points on a function when tangent lines have a given slope
Question
16x3
- 4x2 6x - 13 have a tangent line of slope 5?
For which value(s) of x does f(x) =
3
If there is more than one answer, give all of the x-values separated by commas, e.g. if f (x) has a tangent line of slope 5 at
x = 3 and x = 5 enter 3, 5.
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Determine the points on a function when tangent lines have a given slope Question 16x3 - 4x2 6x - 13 have a tangent line of slope 5? For which value(s) of x does f(x) = 3 If there is more than one answer, give all of the x-values separated by commas, e.g. if f (x) has a tangent line of slope 5 at x = 3 and x = 5 enter 3, 5.

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Expert Answer

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Step 1

Find value of x for the given function.

Given
16x3
-4x-+6x-13
f(x)
3
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Given 16x3 -4x-+6x-13 f(x) 3

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Step 2

Differentiate f w.r.t x,

df d16x3 4x2+6x-13
dx dx
d
d
d 163 d
-4x2+"6x-"(13)
dx
3
dx
dx
16
2-4x2x+6
3x2-4x2x+6
3
df -16x2-8x+6---I)
dx
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df d16x3 4x2+6x-13 dx dx d d d 163 d -4x2+"6x-"(13) dx 3 dx dx 16 2-4x2x+6 3x2-4x2x+6 3 df -16x2-8x+6---I) dx

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Step 3

Given: Slope...

(i.e.)5
dx
Substitute slope in equation ()
df16x2-8x+6
dx
5 -16x2-8x+6
16x2-8x+1 0
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(i.e.)5 dx Substitute slope in equation () df16x2-8x+6 dx 5 -16x2-8x+6 16x2-8x+1 0

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Tagged in

Math

Calculus

Derivative