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tangents and normals at what points will the tangents to the curve y = 2x^3 – 15x^2 + 36x – 21 be parallel to x axis? also find the equations of the tangents to the curve at these points

tangents and normals
at what points will the tangents to the curve y = 2x^3 – 15x^2 + 36x – 21 be parallel to x axis? also find the equations of the tangents to the curve at these points

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

y = 2x^3 - 15x^2 + 36x - 21
Slope of tangent: y’ = 0
y' = 2.3x^2 - 15.2x + 36 = 0
6x^2 - 30x + 36 = 0
x^2 - 5x + 6 = 0
(x-3)(x-2) = 0
\Rightarrow x = 2, 3
Find the corresponding y and thats gonna be the eauation of tangents.
x = 2
y = 2.2^3 - 15.2^2 + 36.2 - 21
y = 16 - 60 + 72 - 21 = 7

x = 3
y = 2.3^3 - 15.3^2 + 36.3 - 21
y = 54 - 135 + 108 - 21 = 6
y = 6 and y = 7 are equation of tangents.

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