Question

Instantaneous rate of change of f(x) with respect to x at x = a is defined as $f^{\prime }\left(x\right)={lim}_{h\to 0}\frac{f\left(a\right)-f(a+h)}{-h}$ [its give that the limit exists ]

• A. True
• B. False

Answer 1

The correct option is A

True

The instantaneous rate of change of f(x) with respect to x is defined as $f^{\prime }\left(x\right)={lim}_{h\to 0}\frac{f(a+h)-f\left(a\right)}{h},$ provided the limit exists. We multiply both numerator and denominator by -1 to get the given expression in question. That is${lim}_{h\to 0}\frac{f\left(a\right)-f(a+h)}{-h}$.So, the given statement is correct In this question we check if you are clear with definition of instantaneous rate of change