Tamil Nadu Board of Secondary EducationHSC Arts Class 12th

# Using the Rolle’s theorem, determine the values of x at which the tangent is parallel to the x-axis for the following functions: f(x)=x-x3,x∈[0,9] - Mathematics

Sum

Using the Rolle’s theorem, determine the values of x at which the tangent is parallel to the x-axis for the following functions:

f(x) = sqrt(x) - x/3, x ∈ [0, 9]

#### Solution

f(x) = sqrt(x) - x/3, x ∈ [0, 9]

f(0) = 0, f(9) = sqrt(9) - 9/3 = 3 – 3 = 0

⇒ f(0) = 0 = f(9)

f(x) is continuous on [0, 9]

f(x) is differentiable on (0, 9)

Now f'(x) = 1/(2sqrt(x)) - 1/3

Since, the tangent is parallel to x-axis.

f'(x) = 0

1/(2sqrt(x)) - 1/3 = 0

⇒ 1/(2sqrt(x)) = 1/3

sqrt(x) = 3/2

x = 9/4

x = 9/4 ∈ (0, 9)

Concept: Mean Value Theorem
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#### APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 12th Mathematics Volume 1 and 2 Answers Guide
Chapter 7 Applications of Differential Calculus
Exercise 7.3 | Q 2. (iii) | Page 21
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