SATHEE: Application of Derivatives 4 Question 40

Application of Derivatives 4 Question 40

####42. If $f (x)$ is twice differentiable function such that $f (a) = 0$ , $f (b) = 2, f (c) = 1, f (d) = 2, f (e) = 0$ , where $a < b < c < d < e$ , then the minimum number of zeroes of $Missing or unrecognized delimiter for \left$ in the interval $[a, e]$ is

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Answer:

Correct Answer: 42. $P_{0} = \frac{1}{2}, \frac{5}{4}$ and $Q_{0} = \frac{5}{4}, \frac{1}{2}$

Solution:

Let $g (x) = \frac{d}{d x} [f (x) \cdot f^{'} (x)]$

To get the zero of $g (x)$ , we take function

$h (x) = f (x) \cdot f^{'} (x)$

between any two roots of $h (x)$ , there lies atleast one root of $h^{'} (x) = 0$ . $\Rightarrow g (x) = 0 \Rightarrow h (x) = 0$

$\Rightarrow f (x) = 0$ or $f^{'} (x) = 0$

If $f (x) = 0$ has 4 minimum solutions.

$f^{'} (x) = 0$ has 3 minimum solutions.

$h (x) = 0$ has 7 minimum solutions.

$\Rightarrow h^{'} (x) = g (x) = 0$ has 6 minimum solutions.

Application of Derivatives 4 Question 40

Answer:

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Application of Derivatives 4 Question 40

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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