Applications of Derivatives
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The function, f(x) = (3x – 7)x²/³, x ∈ R, is increasing for all x lying in:
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The function, f(x) = (3x – 7)x²/³, x ∈ R, is increasing for all x lying in:
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f (x) = (3x - 7)x²/³
⇒ f (x) = 3x? /³ - 7x²/³
⇒ f' (x) = 5x²/³ - 14/ (3x¹/³)
= (15x - 14) / (3x¹/³) > 0
∴ f' (x) > 0 ∀x ∈ (-∞, 0) U (14/15, ∞)
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If is a point at which Rolle's theorem holds for the function, in the interval , where , then is equal to:
If is a point at which Rolle's theorem holds for the function, in the interval , where , then is equal to:
f(3)=f(4) ⇒ α=12
f'(x) = (x²-12)/(x(x²+12))
∴ f'(c)=0 ⇒ c=√12
∴ f''(c) = 1/12
Upvote If the lines x+y=a and x-y=b touch the curve y=x²-3x+2 at the points where the curve intersects the x-axis, then a/b is equal to
If the lines x+y=a and x-y=b touch the curve y=x²-3x+2 at the points where the curve intersects the x-axis, then a/b is equal to
0.50
y = x²-3x+2, x+y=a, x-y=b
x?=2 x?=1
y? = 4-6+2 = 0 y?=0
(2,0)
(1,0)
b=2
a=1
∴ a/b = 1/2 = 0.5
Upvote Which of the following point lies on the tangent to the curve x⁴eʸ + 2√(y+1) = 3 at the point (1,0)?
Which of the following point lies on the tangent to the curve x⁴eʸ + 2√(y+1) = 3 at the point (1,0)?
e? y'x? + 4x³e? + 2y' / (2√ (y+1) = 0 at (1,0)
y' + 4 + y' = 0 ⇒ y' = -2
equation of tangent at (1,0) is 2x + y - 2 = 0
So option (C) is correct.
Upvote What are the important formulas in Class 12 Applications of Derivatives?
The Class 12 Applications of Derivatives chapter is mainly focused on the usage of derivatives rather a lot formulas. Students can check the important formulae below;
- Rate of Change of a Quantity
If , then the rate of change of with respect to is:
- Increasing and Decreasing Functions
A functio
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