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Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsNumber of Solutions (graph)Medium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

$f (x)$ is a continuous and differentiable function. Given that $f (x)$ assumes values of the form ±√I where 'I' denotes the set of whole numbers whenever $x = a$ or $b$ ; otherwise, $f (x)$ assumes real values. Also, f(c) = −3/2 and |f(a)| ≤ |f(b)|. The graph of $y = f (x) \cdot f^{'} (x)$ is given below.

Using the above data, answer the following:

The number of values that $(f (a))^{2} + (f (b))^{2} + (f (c))^{2}$ can assume is

Options:

Answer:

Solution:

$f (x) \cdot f^{'} (x) \geq 0$ in $[a, c]$ and $\leq 0$ in $[c, b]$ . $f (c) = - 2$ and $f (x) f^{'} (x) \neq = 0$ in $(a, c) \cup (c, b)$ . $f (a), f (b) \leq 0$ .

$f (a) 000 - 1 - 1 - 2 f (b) 0 - 1 - 2 - 1 - 2 - 2 f (c) \frac{- 3}{2} \frac{- 3}{2} \frac{- 3}{2} \frac{- 3}{2} \frac{- 3}{2} \frac{- 3}{2}$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Number of Solutions (graph)

⏱ 2mℹ️ Source: QB

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