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02/23/2023 · Primary School

sider the function \( f(x)=4-5 x \) near \( x=1 \) (a) Simplify the difference quotient as much as possible: \( \frac{f(1+h)-f(1)}{h}=\square \) Hint: Cancel \( h \) from numerator and denominator. (b) Use your result from (a) and the limit definition of the derivative to calculate \( f^{\prime}(1)=\lim _{h \rightarrow 0} \frac{f(1+h)-f(1)}{h}=\square \boldsymbol{\Sigma} \) of the line defined by \( y=4-5 x \). (c) The value of \( f^{\prime}(1) \) in part (b) is equal to the