Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The problem is:

If $f(x) = -4x + 5$, find $\dfrac{f(a + h) – f(a)}{h}$

share|improve this question

closed as off-topic by dragon, Kirill, Fundamental, Davide Giraudo, Hakim Jun 25 '14 at 20:57

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – dragon, Kirill, Fundamental, Davide Giraudo, Hakim
If this question can be reworded to fit the rules in the help center, please edit the question.

What have you tried? For example, what is $f(a+h)$ for the function $f(x)$ you gave us? –  Tom Jun 25 '14 at 19:27

2 Answers 2

If someone says $f(\color{red}{\mathrm{something}})$, they are telling you to take the formula of $f(x)$, and everywhere that appears $x$, you put $\color{red}{\mathrm{something}}$ instead. For example, if $f(x) = x^2 + 1$, $f(\color{red}{a+h})$ would be $(\color{red}{a+h})^2 + 1$. Can you do the same with the function you have there? (:

share|improve this answer

$$\eqalign{\tt f(\color{blue}x)=-4\color{blue}x+5 \ \ &\rlap{\rlap{=}=}{\ >}\tt \ \ f(\color{blue}{a+h})=-4\color{blue}{(a+h)}+5=-4a-4h+5 \\ &\rlap{\rlap{=}=}{\ >} \ \ \tt f(\color{blue}a)=-4\color{blue}a+5. }$$ Therefore: $$\eqalign{\tt \dfrac{f(a+h)-f(a)}{h} &= \tt \dfrac{-4a-4h+5-(-4a+5)}{h}\\ &=\tt\require{cancel}\dfrac{\cancel{-4a}-4h+\cancel5+\cancel{4a}\cancel{-5}}{h}\\ \tt &=\tt \dfrac{-4h}{h} =-4.\tag{$\tt h\neq0$}\\ }$$

share|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.