A function f is defined as follows:f(x) = beg | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For $f(x)$ to be derivable at $x = c$,it must first be continuous at $x = c$.$1$. Continuity at $x = c$:$\lim_{x 	o c^-} f(x) = \lim_{x 	o c^+}

Vedclass · Accepted Answer

$a = \cos c, b = \sin c - c \cos c$

Vedclass · Answer

(C) For $f(x)$ to be derivable at $x = c$,it must first be continuous at $x = c$.$1$. Continuity at $x = c$:$\lim_{x 	o c^-} f(x) = \lim_{x 	o c^+} f(x) = f(c)$$\sin c = ac + b$  --- (Equation $1$)$2$. Differentiability at $x = c$:$f'(x) = \begin{cases} \cos x & 	ext{if } x  c \end{cases}$For $f'(c)$ to exist,the left-hand derivative must equal the right-hand derivative:$\lim_{x 	o c^-} f'(x) = \lim_{x 	o c^+} f'(x)$$\cos c = a$$3$. Substituting $a = \cos c$ into Equation $1$:$\sin c = (\cos c)c + b$$b = \sin c - c \cos c$Thus,$a = \cos c$ and $b = \sin c - c \cos c$.

$A$ function $f$ is defined as follows:
$f(x) = \begin{cases} \sin x & \text{if } x \le c \\ ax + b & \text{if } x > c \end{cases}$
where $c$ is a known quantity. If $f$ is derivable at $x = c$,then the values of $a$ and $b$ are . . . . . . and . . . . . . respectively.

Similar Questions

The set of all those points,where the function $f(x) = \frac{x}{1 + |x|}$ is differentiable,is

If $f(x)$ is a differentiable function such that $f: R \to R$ and $f\left( \frac{1}{n} \right) = 0$ for all $n \ge 1, n \in I$,then:

If $f(x) = \begin{cases} e^x + ax, & x < 0 \\ b(x - 1)^2, & x \ge 0 \end{cases}$ is differentiable at $x = 0$,then $(a, b)$ is

If $y = \sec^{-1} \left( \frac{2x}{1 + x^2} \right) + \sin^{-1} \left( \frac{x - 1}{x + 1} \right)$,then $\frac{dy}{dx}$ is equal to

Let $\alpha, \beta \in R$ be such that the function $f(x) = \begin{cases} 2 \alpha (x^2 - 2) + 2 \beta x, & x < 1 \\ (\alpha + 3) x + (\alpha - \beta), & x \ge 1 \end{cases}$ is differentiable at all $x \in R$. Then $34(\alpha + \beta)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$A$ function $f$ is defined as follows:$f(x) = \begin{cases} \sin x & \text{if } x \le c \\ ax + b & \text{if } x > c \end{cases}$where $c$ is a known quantity. If $f$ is derivable at $x = c$,then the values of $a$ and $b$ are . . . . . . and . . . . . . respectively.