Question

Which expression defines the derivative of a real function \[f\] at a point \[c\] in its domain?

Options

• \[f'(c)=\lim_{h\to0}\frac{f(c)-f(c+h)}{h}\]

• \[f'(c)=\lim_{h\to0}\frac{f(c+h)+f(c)}{h}\]

• \[f'(c)=\lim_{h\to0}\frac{f(c+h)-f(c)}{h}\]

• \[f'(c)=\lim_{h\to c}\frac{f(c+h)-f(c)}{h}\]

Answer 1

The derivative at \[c\] is defined by the limit of the difference quotient as \[h\to0\]. The numerator must be \[f(c+h)-f(c)\], and the denominator is \[h\].