The derivative of a function f(t) at the point (a, f(a)) can be given by:
$f'(a) = \lim_{h\rightarrow 0} \dfrac{f(a+h)-f(a)}{h}$ f'(a) = \lim_{h\rightarrow 0} \dfrac{f(a+h)-f(a)}{h}.
Choose the correct statement/s below regarding the derivative.

Question

The derivative of a function   f(t)  at the point   (a, f(a))  can be given by:  f'(a) = \lim_{h\rightarrow 0} \dfrac{f(a+h)-f(a)}{h} . Choose the correct statement/s below regarding the derivative.

Accepted Answer

The derivative of a function at the point   (a, f(a))  is the gradient of the tangent line at that point.

Answer

The derivative does not exist when   h=0  as we cannot divide by zero.

Answer

If the function describes the distance of a particle from the origin after time   t , then the instantaneous velocity at time   t=b  can be given by    \lim_{h\rightarrow 0} \dfrac{f(b+h)-f(b)}{h} .

Answer

If the function describes the distance of a particle from the origin after time   t , then the instantaneous velocity at time   t=b  can be given by    \lim_{h\rightarrow 0} \dfrac{f(a+b)-f(a)}{h} .

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