Let f(x) be a continuous and differentiable f | vedclass

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

Question

(C) By the definition of the derivative,$f'(x) = \lim_{h 	o 0} \frac{f(x + h) - f(x)}{h}$.Given the functional equation $f(x + h) = f(x) - 3xh + f(h)

Vedclass · Accepted Answer

$-3x + 7$

Vedclass · Answer

(C) By the definition of the derivative,$f'(x) = \lim_{h 	o 0} \frac{f(x + h) - f(x)}{h}$.Given the functional equation $f(x + h) = f(x) - 3xh + f(h)$,we substitute this into the limit expression:$f'(x) = \lim_{h 	o 0} \frac{f(x) - 3xh + f(h) - f(x)}{h}$.Simplifying the expression,we get:$f'(x) = \lim_{h 	o 0} \frac{f(h) - 3xh}{h}$.$f'(x) = \lim_{h 	o 0} \left( \frac{f(h)}{h} - 3x ight)$.Given that $\lim_{h 	o 0} \frac{f(h)}{h} = 7$,we substitute this value:$f'(x) = 7 - 3x$.

Let $f(x)$ be a continuous and differentiable function for all real numbers such that $f(x + y) = f(x) - 3xy + f(y)$. If $\lim_{h \to 0} \frac{f(h)}{h} = 7$,then the value of $f'(x)$ is:

Similar Questions

$A$ chloro compound of vanadium has a spin-only magnetic moment of $1.73 \ BM$. This vanadium chloride has the formula: (Atomic number of $V = 23$)

$A$ coordination complex contains $Co^{3+}$,$Cl^{-}$,and $NH_3$. When dissolved in water,one mole of this complex gives a total of $3$ moles of ions. The complex is

Electrons with de-Broglie wavelength $\lambda$ fall on the target of an $X$-ray tube. The cut-off wavelength of the emitted $X$-ray is:

During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_P / C_V$ for the gas is

Anoxygenic photosynthesis is characteristic of

Vedclass Test Series

Exam Paper Generator

Online Exam Module